I moved from WI to NM with 2 cats.
My mom came with me. We rented a U-haul and towed a trailor for my car. So, mom, myself, and 2 cats all in the front of the U-haul.
We did spend an overnight in a hotel, so the cats had their litterboxes at night.
I don't like the idea of ever letting the cats out of the carriers in the car, I've heard too many sad stories about that. So, I kept mine drugged on acepromazine and in their carriers at all times. They slept the whole trip. They'd each wake up for a few minutes every hour or so and meow to let us know how unhappy they were with the whole thing, but for the most part they just slept.
Just beware, many rental places will say no pets. We did it anyways though. We also snuck them into the hotel with us.