We've done it too many times... Virginia to Virginia (two hours), Virginia to Mississippi (2 days), Mississippi to Oklahoma (10 hours), and Oklahoma to Washington (5 days). And one plane flight from Washington to New Jersey. And they once went from Mississippi to New Jersey and back.
Anyway... My cats are obsessed with each other, so we bought a medium dog crate, cut a piece of plywood to fit in (with a gap) so they had two "stories." The plywood is padded, of course. Wouldn't want their highnesses to suffer. On the bottom floor we have the litter box and the food and water. They like to see things, so they usually sit on the top floor and watch the cars go by. Neither has ever gotten car sick, and we only tried tranqs once. (Didn't work.) Oh, and I also put a plastic shower curtain around the edges by the litterbox so they wouldn't spray on the car if they get jostled while peeing. Though as I recall, they never used the box in the car - just held it all till the hotel.
We always got fast food and never stopped for long, so they weren't left in the car more than the couple of minutes to go potty or whatever. (Though we haven't driven with the toddler and the cats, which would be harder on breaks.)
The hardest part was getting them in and out of the hotels. The last trip, I was just carrying them in and out, but by the end of the trip, they were fighting me hard. (The crate is too heavy and awkward to lift.) I think next time we drive, we'll bring a same carrying crate to take them to and from the hotel. Finding a cat-friendly hotel is getting easier, though always ask - some charge extra for them, and others require you to stay in a smoking room.
When you get them to their new home, confine them in one room with their box and other familiar stuff (bedding, toys, toddlers...

) for a couple of hours until them get used to the smells of the new house. Obviously, keep them locked up when you're actually moving in furniture and boxes, so they don't decide to sneak out and look for their old home.
Good luck! It's really not that bad. Just give them lots of love and reassurance.