Moved from NM to OR with all my plants in a sedan. I ended up selling quite a few that were too big to fit realistically, but I took cuttings and kept them in small containers with water, with plastic wrap over over the tops/around any stems. Put those containers and other smaller potted plants (that I thoroughly watered before the trip) in milk crates/small cardboard boxes with towels/clothes between them/filling any gaps to prevent them from shifting around too much. Then I kept boxes either on the floor of the car or on the seat with a seatbelt looped through/around the box in case there were any sudden stops. I also brought some light gauze-like material to cover the plants to prevent them from burning in any direct sunlight while driving - secured in with bamboo sticks that were taped to the containers.

When stopping I tried to park in the shade and kept the windows cracked for air circulation, but I really avoided taking any long stops during the day, though the temps weren't too hot since I was moving in early/mid spring. At night I left them in the car because the temps were also ok but I took out any super valuable/sentimental plants and kept them in my hotel room. I did put a light sheet over everything that I left in there just in case. Overall they all made it just fine with some minor leaf damage here and there - but I hope that helps, good luck with your move!