My seven year old dog got carsick when he was younger. Nerves and motion sickness combined. I tried really hard to get him used to the car but it really went away when his crate was raised up so he could see out the window better. I trained him to accept the car with clicker training. That got him to trust me enough to get in even if not happy about it. Now, after six years he does ask to go in the car!
You could try baby steps like I did. Practice your journey in tiny steps. Pick up cat. Pick up cat and put in crate/carry to door [whichever you decide to do] return to a safe happy place and reward cat for being so brave. PUC, CTD, open door. Then do all the previous steps and take one step outside. The chain going all the way to backing the car down the driveway might have 20-30 steps! With each step go back to a safe comfortable place and reward the cat. It sounds tedious but it will go quickly until you find the sticking point. That sticky scary place could be stepping out the door or turning the car on.
I would not want to travel with a carsick cat out of a crate. Back when, my scared cat would actually crawl under the seat then under my feet when in the car - he was a fat guy! What about fixing up a mesh bottom so any sick would not be under foot? I did travel eight hours in a heavy rain storm with a yowling cat in a cardboard carrier many years ago. Better than a sick cat any day! Oh, out of a carrier there could be an escape. You probably won't have to stop during a three hour trip but that would be a nightmare.
I strongly feel it isn't fair to an animal to expect it to be comfortable in brand new situations without preparation. It is really hard with cats as generally they stay home and go in the car to the vet once or twice a year. Dogs go to work, hikes, the park in cars all the time. Hope you have a chance to get your kitty used to cars. If not happy still, get the sedation!