The trip itself shouldn't be too bad. How does your cat react when you take him to the vet? Try to figure out if he enjoys looking out the window or if seeing everything going by freaks him out. Some animals get more car sick if they can't see out, others if they can. For a long trip I use a crate large enough for the cat and a small litterbox. About an hour before you get ready to leave, feed the cat and give him time to use the litterbox before placing him in the crate. You can offer food/water during the trip but most animals are too nervous to eat or drink. You'll have to figure out what works best for your pet but I've found elevating the crate and then covering half of it gives my pets the security they need. My DM's cat meowed a lot when we had to travel with her but when we put the small, soft carrier up in the rear window and opened one end she was happy as could be. She never left the carrier and never meowed again. (We opened one end because she'd been in the carrier for 8+hrs after air travel)
Since you'll be dealing with moving during this time, I would suggest you board the cat during the whole moving process if you don't have a secure room to keep him in. Many animals disappear on moving day.

I usually give my animals free reign in the motel room and if I have to leave I put a 'Do not disturb' sign on the door. I also don't allow maid service unless I leave the room and take the pet with me.

Before the move, one thing you may want to try is to get your cat used to wearing a harness.....then later attach a leash and let him drag it around to get used to it. That will give you control of him if you ever need to let him out within the car or elsewhere. Depending on your pet, you may be able to give him the whole back seat if you can secure him with harness and leash.

Thank you annz. You provided a lot of good advice and I appreciate your time. My cat is scared of strangers and hides when someone he doesn't know comes over. My small suv will be packed to the limit so I will not have lots of space to move him around.

Last time I moved, my cat was fine shut up in the bathroom while the movers were there. Then she fled to the basement, I think in shock from hearing all the moving noises and then coming out and seeing the apartment empty, as I was cleaning up and it took me three hours to coax her from behind the water heater.

I only had to go 300 miles and she meowed the entire way, which is normal for her on car trips.

Do check with your motel--some do not allow pets. What I did in the motel was set up her litter box in the bathroom. When I had to leave briefly for meals and such, I shut her in the bathroom with food and water--I was terrified she'd make a break for the door and I'd never see her again. She did not seem to mind being imprisoned in the bathroom. Frankly, she was not coping with the whole move very well and seemed content to stay in a small space.

On moving-in day, I again shut her in the bathroom of the new apartment, with a sign on the door so people would open it with caution. Once the movers were gone and she was set free, she found my bedroom and stayed under the bed, with brief trips for food, water and the litter box, for the next day or so. Eventually, she came out and explored the entire apartment and claimed the best window sill for sunning and the comfy chair for naps.

I helped my friend move two of her cats to New Mexco from Northern California - two nights in Motel 6. We made certain they had their own crates, with a favorite towel or blanket with my friends scent on it and a water bowl. The cats howled for the first hour, got tired settled in and all was well. Anytime we stopped we made sure to park them in deep shade, tho I dont think you hafta worry about that this time of year.
We stopped at Motel 6, she brought in all of her luggage, set up the kitty litter box and let the cats out to roam the room, being very careful when the door opened that they did not sprint out.
In the morning, she put them in their crates to feed them, making it easier for us when I arrived to help load up the car.

Another thing- when I traveled with mine(they did great BTW) I made sure that they both had on a collar in which I had securely attached a note(with much tape) that had all my contact info, and that of my son whom we were visiting, and that they were diabetic, to only give them canned food if found.

Just in case they were to have escaped.

When I emigrated I just popped my cat in his basket and drove. We got some funny looks checking the car in at the docks, the cat in the basket was on the wife's lap! But we'd taken him away in the past, he had been to motels with us (never let out of course) so this was a bit more of a jollie for him, being taken to foreign manors. Left the windows open a bit on the car while at sea so he'd be comfortable. When docking at the far side he was fine. There wasn't even any toilet mess.

He embraced our new life abroad, catching mice from day one at our new house, and lived to a good age for a cat, 14 years. It was very hard when in 2011 I had to have the vet put him to sleep but it wasn't long before my house once more became catty.

I drove from San Francisco to Cincinnati with my cat (and a friend) in summer. Before leaving that morning, I made the mistake of giving him some drug (don't remember, it was 20 years ago) to "calm" him down. He was a zombie. I found that he was perfectly happy being in a crate, up high enough in the car to be able to see out. He got his freedom at night in the motels.
A few weeks later, I made the trip from Cincinnati to Baltimore and he did fine. We spent 3 weeks in an empty apartment waiting for furniture to arrive. I set my cat up in a linen closet with a blanket and left it part way open, litter box in the bathroom. We both survived.
Good luck on your trip.