My cats always travel in a kennel, and the dogs have safety harnesses that fasten to seatbelts. A loose animal becomes a projectile in an emergency stop and can become injured or injure someone else. They also cannot get under foot at an inopportune moment.
Have you tried using a pheromone spray like Feliway? I give the inside of the kennel two or three squirts just before I load the cats.
My two elderly (16 & 18) Siamese are not really fond of travel. They are fine once we get to our destination and they can settle in on the bed but find the travel stressful. The Feliway really helps
FeliwayThere are other, herbal calming products, but Feliway works well enough for us that I have not tried them.