We recently moved from Idaho to NC. I had our 2 adult cats in my car, and they're both different passengers. I kept them both in a very large carrier with mesh screening for the first hour, then opened the screening on one side. One was out and about and the other very content to stay put. Litter box available in the car (I showed them where it was), food/water available, although they didn't use either. Took them into the hotels in the carrier, got the litter box/food/water set up and let them roam the room. They were fine. Same routine every day.
There is a spray you can buy at pet supply stores with kitty pheromones. Very lightly scented to humans, but calms the anxiety in cats. Seemed to work somewhat, and with no
drugs! Not as effective as valium, but safer!