Congrats to you for standing up to the vet (and the assistant!)
As for the drive - I had 2 cats my last year in college that rode with me 4 hours to my parents' house from time to time, and back & forth when I was visiting friends after graduation. They also rode with me several times from the IL/WI line to NC. Ronnie used to get carsick the first hour, (into a cup!), and was fine for the rest of the 20 hr trip. Elsie rode under the drivers seat, and promptly found her spot under the covers at the hotel. Litter box in back seat. No other issues. They put LOTS of miles on their kitty belts... and even went "to the Falls" - REALLY!!! - as in Niagra, after my sister's wedding!!! We did a 30 minute tour on Maid of the Mist and got back to find them ready to have more than a window cracked. Elsie lived to be 18, Ronnie (the tri-pod PTS w/ recurring cancer) so I'm guessing all the travel didn't hurt either!
Your kitty will adapt - and might even enjoy travelling! I had a friend who took her cat to the beach every weekend. She said the cat knew where they were better than a GPS (smell those fishies!!!). Rode on the back of the seat.
One word of caution, however. If your car has power windows, LOCK THEM!!! I drove to a friend's house once and Mardi enjoyed her seat on the passenger headrest until she decided to open the rear window at 60 mph in the rain! :shock: I grabbed her by the tail and she clung to my chest like glue for the rest of the ride! When we got to my friend's house, she didn't come out from behind the toilet for 3 days!!! Lock the windows! :lol: