My family moved the whole zoo (3 cats, 3 kids, 1 pug) from the midwest to the east coast last winter. The two adult cats and the pug rode together in a nice big dog crate that could hold them all comfortably, which was wrapped in blankets and wedged securely in the back of a Jeep riding on a car trailer (the kind that keeps all four wheels off the road, so it's level.) The kitten rode by himself in his own carrier in the cab of one of our U-Haul trucks.
The big boys were famous for nonstop meowing in cars, so riding in the otherwise unoccupied Jeep-in-tow saved everyone's ears. Actually, they traveled quite calmly. It seems that if they have no one to complain to, they just sit tight and wait. The pug was a little confused, because they tended to lay on top of him, which wasn't typical. I doubt if it was due to cold; every time I checked them it was nice and cozy warm back there. I think they just decided he wiggled too much and held him down...
Seriously, you have to consider their environment carefully on long trips. A closed vehicle in warm weather can get dangerously hot. A comfortably heated car in winter for us humans can still be too hot for the furry ones, especially with travel stress. The Jeep was a convertible, so it tended to stay cool but not cold in the sun in winter. With blankets around the carrier, the animals had a nice 50-60 degree temperature all the time, plus they didn't have to deal with the noisy, unfamiliar-smelling truck cabs. that would have caused more stress. We made frequent stops to check on them (besides, the kids had to pee!) and the cats were frequently napping, and were only marginally interested in what was going on when we let the pug out to do his business. So, we never needed any tranquilizers; they settled into the trip just fine as long as they were comfortable.
Hotels were the real adventure. Pet-friendly hotels are not always available, so checking in and out was interesting. Basically, the animal crates were kept covered, and the "fuzzy children" were kept calm and quiet. (Kitty and doggy treats are a good thing...) and they were quickly wheeled in underneath a mountain of luggage past the unsuspecting desk clerk. The litter box (an Omega-Paw self cleaning one) was kept in a big plastic trash bag, and also buried under other luggage on the cart, so it was just another nondescript package.
In hotel rooms, the pug was quiet as always, and good about slipping outside to do his business without any fuss. The Omega-Paw box is easy to clean out, and the pull-out waste tray dumps into small plastic bags easily. No one ever knew we were traveling with pets unless we said something.
Bathroom stops weren't much of an issue. The pug went out on his leash at rest stops while the kids went to the restrooms, too. The cats would "hold it" because they're not completely sure of their surroundings on the road. As soon as we got them in the hotel room and brought out their familiar litter box,though, they lined up and took turns. Kind of funny to watch, really, because they looked just like people waiting semi-patiently in a long restroom line!
