Can we refuse to allow employees to travel the way they wish?

Q: “Every year we send our sales staff to a couple of trade shows, mainly in Las Vegas. We book the flights and lodgings, pay mileage to and from the airport, pay for all meals and all hours worked at the trade show, plus overtime. We reimburse for any incidental expenses that may be incurred by the employees. Our 'star' employee prefers to drive next time instead of flying; this would mean an extra expense for our small company (for the longer travel time, extra meals, extra lodging and extra mileage). When we said no, everyone is flying, the employee replied that he would drive on his own dime. We do need this employee at the trade show, but it is not cost-efficient for us. I just want to make sure that we are not violating any labor laws by saying everyone must fly to this particular show (due to the distance), with no exceptions.”  – Nora, Wyoming