Hudson Specialty Insurance Company issued a Commercial Lines Master Policy to Sonic Insurance Advisory Trust providing commercial general liability and commercial property insurance to Sonic Restaurants, Inc. and to Sonic franchisees who were enrolled members of the Trust. One named insured was Brash Tygr, LLC, which owned and operated the Sonic Drive-In restaurant in Carrollton, Missouri. Lloyd and Nancy Miller sued Brash Tygr and its principals in Missouri *588state court to recover damages for substantial personal injuries suffered when a car driven by Tyler Roush, a Managing Member of Brash Tygr, struck Lloyd Miller, a pedestrian. Invoking diversity jurisdiction, Hudson filed this declaratory judgment action against the parties to the state court action seeking a declaration that the Hired and NonOwned Auto Liability endorsement to the policy’s Commercial General Liability Coverage Form provides no coverage to any defendant in the underlying lawsuit. Hudson appeals the district court’s ruling granting summary judgment to defendants on the coverage issue. We reverse that ruling. Defendants cross appeal the court’s earlier ruling that Hudson is not collaterally estopped to contest coverage by the state court judgment in favor of the Millers in the underlying action, to which Hudson was not a party. We affirm that ruling.
I. Background
Hudson’s Hired and Non-Owned Auto endorsement provided, as relevant here:
B. NON-OWNED AUTO LIABILITY We will pay on behalf of the insured all sums that the insured shall become legally obligated to pay as damages because of “bodily injury” or “property damage” arising out of the use of a “non-owned auto” by any person other than you in the course of your business.
Tyler Roush was driving a car he jointly owned with his mother, Sharon Roush, when the accident occurred on August 3, 2009, while Hudson’s policy was in effect. Hudson argues that undisputed facts establish that Tyler Roush was not using the car “in the course of [Brash Tygr’s] business,” so the policy provided no coverage. Defendants argue that undisputed facts establish that Tyler was using the car in the course of Brash Tygr’s business. Defendants have the burden of proof on this coverage issue. See J.E. Jones Constr. Co. v. Chubb & Sons, Inc., 486 F.3d 337, 340 (8th Cir.2007) (applying Missouri law). The following facts are undisputed.
The Accident. Sharon Roush asked Tyler to deposit her paycheck in her personal bank account and to deliver personal mail to the post office. Tyler first traveled from his parents’ home, where he was staying, to the bank and deposited Sharon’s check. Before Tyler left, a bank employee handed Tyler bank deposit bags that the Sonic Drive-In used to make cash deposits. Tyler did not work at the Drive-In and had not intended to pick up deposit bags. Other Brash Tygr representatives periodically retrieved deposit bags, which the bank used for advertising. Brash Tygr could make Sonic deposits without using the bags, and there is no evidence that a Brash Tygr representative ever made a special trip to the bank to pick up deposit bags. Tyler left the bank and put the deposit bags in his car, intending to take them to his parents’ home so that one of them could take the bags to the Drive-In. After leaving the bank, Tyler drove toward the post office, away from the Drive-In but in the direction of his parents’ home. While making a left turn, Tyler struck and severely injured Lloyd Miller in a pedestrian crosswalk.
The Brash Tygr Entity. Brash Tygr is a limited liability company (LLC), organized under Chapter 47 of the Revised Statutes of Missouri to provide its members and managers with the same immunity from personal liability for the liabilities of the LLC that is afforded the shareholders and employees of a business corporation. See Mo.Rev.Stat. § 347.057. The members of each LLC “shall adopt an operating agreement” containing provisions “relating to the conduct of the business and affairs of the [LLC] and the *589rights, powers and duties of its members, managers, agents or employees,” not unlike the Missouri General and Business Corporations Law provision that officers and agents of a corporation “shall have such authority and perform such duties ... as may be provided in the bylaws, or ... by resolution of the board of directors.” Compare Mo.Rev.Stat. § 347.081.1, with, Mo.Rev.Stat. § 351.360.2.
At the time of the accident, Tyler held a five percent ownership interest in Brash Tygr. Roush Investments, owned by Tyler’s parents, George and Sharon Roush, held a seventy percent interest in Brash Tygr, and Tyler’s brother, Brandon Roush, owned five percent. The June 1994 Operation Agreement organizing Brash Tygr was signed by Roush Investments, Tyler, and Brandon, who were named the Original Managing Members. The Agreement provided, “Each Managing Member has the power, on behalf of the Company, to do all things necessary or convenient to carry out the business and affairs of the Company.” In August 2009, Tyler was still a Managing Member but had not worked at the Sonic Drive-In for nineteen years.
The Underlying Lawsuit. Lloyd and Nancy Miller’s state court action asserted individual tort claims against Tyler, Sharon, and George Roush seeking compensatory and punitive damages for personal injury and loss of consortium. The Millers also sued Brash Tygr; Roush Investments, Inc.; Brandon Roush; and another Brash Tygr owner, alleging they were vicariously liable for Tyler’s negligence because he acted on behalf of the Sonic franchise while at the bank. Hudson accepted Brash Tygr’s tender of the defense of the action but reserved the right to contest its duty to indemnify any liability to the Millers. The state court defendants asserted that Tyler was not acting as anyone’s agent at the time of the accident and moved for summary judgment on this question of vicarious liability.
With this motion pending, the parties unsuccessfully attempted to mediate. Hudson rejected plaintiffs’ demand that defendants settle all claims against Brash Tygr and “the Sonic defendants” for Hudson’s policy limit of $1 million. Plaintiffs rejected Hudson’s offer of a “high/low” settlement of $1 million or $300,000, which would depend on whether a jury determined that Tyler was acting “in the course and scope of Sonic’s business.” When the Sonic defendants rejected Hudson’s defense under a reservation of rights and withdrew their motion for summary judgment on the vicarious liability issue, Hudson filed this declaratory judgment action in federal court, naming all parties to the underlying action as defendants.
One week later, the Sonic defendants entered into a settlement agreement with the Millers pursuant to Mo.Rev.Stat. § 537.065.1 Consistent with that agreement, Brash Tygr and Tyler Roush then admitted each of plaintiffs’ thirty-six Requests for Admission in the underlying lawsuit, including an admission “that by picking up the Sonic bank deposit bags that Tyler Roush was conducting the business of Brash Tygr, LLC.” The next day, the state court entered detailed findings of fact and conclusions of law. Citing Corp v. *590Joplin Cement Co., 337 S.W.2d 252, 255 (Mo. banc 1960), as controlling authority, the court concluded that Tyler acted as agent of Brash Tygr when he “made a decision to collect the Sonic bank deposit bags while at the bank,” and that this “concurrent purpose” was an adequate basis to find that the trip was “in the course and scope of agency.” The following day, the court entered its Judgment, reciting that the action “was tried to this Court with all parties represented by counsel” and awarding plaintiffs $5.3 million in compensatory damages against the Sonic defendants and $500,000 in punitive damages against Tyler and Brash Tygr.
II. Hudson’s Appeal — Coverage
The district court granted summary judgment in favor of defendants on the coverage issue, concluding that Tyler Roush was using his car “in the course of [Brash Tygr’s] business” at the time of the accident and therefore Brash Tygr’s liability was covered by the Hired and Non-Owned Auto Liability endorsement in Hudson’s policy. It is undisputed that Tyler was driving a “non-owned auto.” The dispositive question is whether the car was being used “in the course of [Brash Tygr’s] business.” “We review a district court’s decision on cross-motions for summary judgment de novo.” Humphries v. Pulaski Cnty. Special Sch. Dist., 580 F.3d 688, 692 (8th Cir.2009). The parties agree that Missouri law governs this issue.
A. In resolving the coverage issue, it is essential to identify the district court’s proper standard of review in determining the course-of-business question, which has been addressed in relevant Missouri cases in three distinct contexts. First, in the underlying action, the question was critical to whether Brash Tygr was vicariously liable to the Millers on their tort claims, which turned on agency law principles. As Hudson’s settlement offer recognized, the issue if disputed would be a question of fact for a jury. Second, in Corp — the Supreme Court of Missouri decision on which the state court relied in concluding that Brash Tygr was vicariously liable — the Court resolved a claim for workers’ compensation benefits, a statutory regime in which the initial decision-maker is an administrative agency. Consistent with principles of administrative law, Missouri courts review whether the agency’s determination of this fact-intensive issue was “supported by competent and substantial evidence on the whole record,” 337 S.W.2d at 258.
This case involves the third context, where the course-of-business issue determines whether there is coverage under an insurance contract. The question is no less fact intensive, but “[a]s with any other contract, the interpretation of an insurance contract is generally a question of law, particularly in reference to the question of coverage.” D.R. Sherry Constr., Ltd. v. Am. Family Mut. Ins. Co., 316 S.W.3d 899, 902 (Mo. banc 2010). A trial may be needed if there is a disputed issue of material fact, as in State Farm Mut. Auto. Ins. Co. v. Allen, 744 S.W.2d 782, 786-87 (Mo. banc 1988), and Firemen’s Fund Ins. Co. v. Thien, 8 F.3d 1307 (8th Cir:1993). But when the material facts are undisputed, the ultimate question — whether Brash Tygr, the insured, has coverage because Tyler Roush was acting “in the course of [its] business” within the meaning of Hudson’s Non-Owned Auto endorsement—is a question of law for the court. Am. States Ins. Co. v. Porterfield, 844 S.W.2d 13, 14 (Mo.App. 1992); see Ind. Lumbermens Mut. Ins. Co. v. Timberland Pallet & Lumber Co., 195 *591F.3d 368, 377 (8th Cir.1999).2
B. We have found no Supreme Court of Missouri decision interpreting the phrase “in the course of your business” in the context of a non-owned auto endorsement. “When a state’s highest court has not decided an issue, it is up to this court to predict how the state’s highest court would resolve that issue.” Minn. Supply Co. v. Raymond Corp., 472 F.3d 524, 534 (8th Cir.2006). In resolving the issue of Brash Tygr’s vicarious liability in the underlying action, the state court concluded that the “dual purpose” doctrine applied by the Supreme Court of Missouri in Corp, a workers’ compensation case, provided the governing standard. Without citation to Missouri authority, the district court ruled that “the dual purpose doctrine, while instructive [is] not controlling.... Here, liability is not premised on the concept of respondeat superior or traditional principles of agency, but rather Tyler Roush’s status as a Managing Member of a Limited Liability Company.” We disagree.
The Supreme Court of Missouri looks to the purpose behind an insurance policy provision to interpret and apply it. See Columbia Mut. Ins. Co. v. Schauf, 967 S.W.2d 74, 77-78, 79 (Mo. banc 1998); State Farm Mut. Auto. Ins. Co. v. W. Cas. & Sur. Co., 477 S.W.2d 421, 424-26 (Mo. banc 1972). The purpose of non-owned auto coverage in a commercial liability policy is to “protect the named insured under the doctrine of respondeat superior when automobiles not owned by it [are] used in its business.” Linenschmidt v. Continental Cas. Co., 356 Mo. 914, 204 S.W.2d 295, 300 (1947); accord Union Standard Ins. Co. v. Hobbs Rental Corp., 566 F.3d 950, 953-54 (10th Cir.2009) (construing “in connection with [the insured’s] business”). Therefore, the standard applied by Missouri courts in determining whether the insured is vicariously liable should also apply in determining the scope of the insured’s non-owned vehicle coverage. Whether the commercial insured was organized as a business corporation, a partnership, a proprietorship, or a limited liability company is irrelevant to this inquiry.
The state court’s decision to apply the dual purpose doctrine in Corp in deciding whether Brash Tygr was vicariously liable for the tort of its employee or agent, Tyler Roush, was consistent with decisions of the Missouri Court of Appeals in tort cases. See Tuttle v. Muenks, 964 S.W.2d 514, 518-19 (Mo.App.1998), and Cooper v. Gen. Standard, Inc., 674 S.W.2d 117, 120-21 (Mo.App.1984), decisions that we applied as reflecting Missouri law in Fackrell v. Marshall, 490 F.3d 997, 1001 & n. 2 (8th Cir.2007). It is also consistent with the application of the “business affairs” coverage limitation in Farm Bureau Town & Country Ins. Co. of Mo. v. Am. Alt. Ins. Corp., 347 S.W.3d 525, 530-31 (Mo.App. 2011). Likewise, using this workers’ compensation principle in resolving analogous questions of insurance contract interpretation is in accord with established Missouri law. See Ward v. Curry, 341 S.W.2d 830, 836 (Mo. banc 1960) (“In Missouri, the courts consistently turn to the Workmen’s Compensation Act in determining the meaning of the word ‘employee’ as used in exclusion clauses of liability insurance policies”).
For these reasons, we conclude the dual purpose doctrine is controlling Missouri law in determining whether Tyler Roush’s personal errand for his mother had a dual *592purpose that was “in the course of [Brash Tygr’s] business,” triggering Non-Owned Auto coverage under Hudson’s policy. The district court’s contrary conclusion was an error of law.
C. The dual purpose doctrine as adopted in Missouri was expounded by an eminent jurist, Judge (later Justice) Cardozo, in Marks’ Dependents v. Gray, 251 N.Y. 90, 167 N.E. 181, 183 (1929). “Briefly stated, the doctrine is that if the work of the employee creates the necessity for the travel, he is in the course of his employment, even though he at the same time is serving some purpose of his own.” Corp, 337 S.W.2d at 255. The Supreme Court in Corp went on to define the doctrine in greater detail:
it is not necessary that, on failure of the personal motive, the business trip would have been taken anyway by this particular employee- at this particular time. It is enough that some one would have had to make the trip to carry out the business mission. If the trip would ultimately have had to be made, and if the employer got this necessary item of travel accomplished by combining it with the employee’s personal trip, it would be a concurrent cause of the trip, rather than an incidental appendage or afterthought. There is no occasion to weigh the business and personal motive to determine which is dominant.
Id. (emphasis in the original), quoting with approval Gingell v. Walters Contracting Corp., 303 S.W.2d 683, 688-89 (Mo.App. 1957). Missouri appellate courts have consistently applied the doctrine as articulated in Corp and Gingell. See, e.g., McClain v. Welsh Co., 748 S.W.2d 720, 726 (Mo.App. 1988).3
Although the state court purported to apply the dual purpose doctrine, it did not properly apply the doctrine because it made no finding that, if Tyler Roush had not accepted the deposit bags when a bank employee handed him the bags at the bank, “some [employee or agent of Brash Tygr] would have had to make the trip to carry out the business mission.” The absence of such necessity has been the determining factor in numerous cases that refused to apply the dual purpose doctrine. See McMain v. J.J. Connor & Sons Constr. Co., 337 Mo. 40, 85 S.W.2d 43, 45 (1935); Williams v. Servicemaster, 907 S.W.2d 193, 194 (Mo.App.1995) (“The dual purpose doctrine ... requires that the employee’s work create the necessity for travel.”); Wines v. Goodyear Tire & Rubber Co., 246 S.W.2d 525, 530 (Mo.App.1952) (procuring gasoline to use the car in the employer’s business the next day “was merely casual and incidental to a purely personal pleasure trip”); Duggan v. Toombs-Fay Sash & Door Co., 228 Mo. App. 61, 66 S.W.2d 973 (1933); Peerless Ins. Co. v. Roedder, No. 4:08CV729, 2009 WL 211921, at *4 (E.D.Mo. Jan. 23, 2009).
Here, defendants submitted no evidence that some Sonic employee or Brash Tygr agent would have had to make a special trip to the bank for deposit bags if Tyler had not brought them to his parents’ home. And there was undisputed evidence to the contrary. Tyler testified he had never picked up bags. More tellingly, in a December 10, 2010, affidavit, after stating *593that he was the President of Roush Investments, Inc., and had been involved in managing the Carrollton Sonic Drive-In since 1978, George Roush averred: “Prior to and on August 3, 2009, Sonic had numerous bank bags at its disposal and did not make special trips to Carroll County Trust Company to pick up bank bags.... The bank bags themselves were not required to make deposits at Caroll County Trust Company.” (Emphasis added.) On this record, the undisputed facts established that picking up the bags was a matter of convenience, not necessity, for Brash Tygr and the Sonic Drive-In. Tyler’s accepting the unsolicited bags from a bank employee was a “casual and incidental” aspect of a purely personal trip that did not give that trip a dual business purpose under Missouri law. Therefore, at the time of the accident, Tyler was not acting “in the course of [Brash Tygr’s] business” as a matter of law, and Hudson is entitled to summary judgment on the coverage issue.4
III. Defendants’ Cross Appeal— Collateral Estoppel
Defendants cross appeal the district court’s denial of their motion for summary judgment, arguing that the doctrine of collateral estoppel bars Hudson from “relitigating” the coverage issue after the state court ruled that Brash Tygr was vicariously liable to the Millers for Tyler Roush’s negligence. This is an alternative argument in support of the district court’s decision, an unnecessary cross-appeal that “complicates briefing schedules and the number and length of briefs in ways that may generate more confusion than enlightenment.” 15A Wright & Miller, Fed. Prac. & Proc. § 3904 at p. 205 (2d ed.1991). Therefore, we dismiss the cross-appeal but will consider the merits of defendants’ alternative argument in support.
“Interpretation of an insurance policy and application of collateral estoppel are matters of state law.” Allstate Ins. Co. v. Blount, 491 F.3d 903, 908 (8th Cir. 2007). Correctly citing the factors Missouri courts consider in applying collateral estoppel, see James v. Paul, 49 S.W.3d 678, 682-85 (Mo. banc 2001), the district court concluded that Hudson was not in privity with any party in the underlying action because, like the insurer in James, “the Millers, Tyler Roush and Brash Tygr ... had an interest in shifting the obligation to pay damages onto Hudson.” That conclusion was clearly correct. The court further concluded that “Hudson has not had any opportunity, let alone a full and fair opportunity, to litigate coverage issues.” Under Missouri law, the court explained, Hudson could not intervene in the underlying action after Brash Tygr, its insured, rejected Hudson’s offer to defend under a reservation of rights. Thus, “[i]f defendants’ arguments were to be accepted, it would mean that the insurance company would have no forum in which to raise coverage questions.... Missouri case law is clear that collateral estoppel should not be applied where to do so would be inequitable.” We agree. When Hudson’s insured conceded vicarious liability in exchange for the Millers’ agreement to seek recovery of the collusive judgment in a lawsuit asserting bad faith by Hudson, it would be inequitable to bar Hudson from raising its coverage defenses in this declaratory judgment action, or in defense of an action by defendants against Hudson. See James, 49 S.W.3d at 689; Cox v. Steck, 992 S.W.2d 221, 224 (Mo.App.1999).
*594Defendants argue that Hudson is barred by the rule that, in an action to determine coverage, an insurer is bound by the judgment in the underlying action if it had an opportunity to control that litigation but refused to do so. This rule does not preclude the insurer from litigating coverage issues in a later lawsuit. See Drennen v. Wren, 416 S.W.2d 229, 234-36 (Mo.App.1967); Cox, 992 S.W.2d at 226. Moreover, defendants cite no authority for their contention that the rule applies when the insurer, rather than wrongfully refusing to defend, has its on-going defense under a reservation of rights terminated by the insured, who then enters into a § 537.065 settlement agreement and, acting in its conflicting self-interest, conspires with plaintiffs in the underlying action to preclude the insurer from litigating its coverage defenses. See James, 49 S.W.3d at 689; Cox, 992 S.W.2d at 225. At the critical stages of the underlying action in this case, Hudson was deprived of its “opportunity to control and manage” that litigation. Schmitz v. Great Am. Assur. Co., 337 S.W.3d 700, 709 (Mo. banc 2011).
IV. Conclusion
In appeal No. 13-1688, we conclude that Hudson is entitled to summary judgment declaring that Commercial Lines Master Policy No. HQSR020001 provides no coverage for the claims asserted in the underlying lawsuit because defendant Tyler Roush was not acting in the course of defendant Brash Tygr’s business within the meaning of the Policy’s Hired and Non-Owned Auto Liability endorsement.
We dismiss the appeal in No. 13-1742. We further conclude the district court correctly ruled that defendants are not entitled to summary judgment on the basis of collateral estoppel and therefore affirm the court’s Order filed March 30, 2012.
The judgment of the district court is reversed, and the case is remanded for the entry of a final judgment consistent with this opinion.
. Section 537.065 permits a plaintiff and "a tort-feasor” to agree, “in consideration of the payment of a specified amount," that plaintiff will limit recovery on any judgment to assets and insurance policies specified in the agreement. The Millers agreed not to collect a favorable judgment from the assets of the Sonic defendants “unless and until Plaintiffs and Defendants have exhausted all reasonable efforts to collect the total amount of said judgments from [Hudson] through the filing and prosecution of a garnishment action and a 'bad faith’ lawsuit against Hudson.”
. In this regard, the Millers as "tort claimants stand in the shoes of the insured.” Allen, 744 S.W.2d at 786.
. An important limitation is that the dual purpose doctrine does not apply "[wjhere at the time of an accident the servant or agent deviates or departs from the usual or most direct route which he would ordinarily follow in using the car on the owner's business, and goes off on some errand or for some purpose wholly his own.” Persons v. Kay's Home Cooking, Inc., 830 S.W.2d 46, 49 (Mo.App. 1992) (quotation omitted). Here, the parties vigorously debate whether Tyler's trip to the post office was such a deviation. We need not resolve this issue.
. Because of our resolution of this issue, we need not consider Hudson’s alternative contention that it was relieved of any liability by Brash Tygr’s failure to notify Hudson of the Millers’ Second Amended Petition in the underlying action.