When I travel with my cat, the carrier is just big enough for him to stand up in and turn around. He doesn't need a lot of space. A nice soft padding at the bottom of the carrier to keep him comfortable.
He did not travel well. He cried and meowed and threw up alot. He got food and water the night before and then took it away. He wouldn't get any food until we stopped for the night. We'd offer water but most of the time he wouldn't drink. WE did get prescription pills from the vet to give him that would knock him out if we could get him to take them.
Don't let him outside even with a harness. Mine did not like the harness and could always wiggle out of it unless I tightened it so tight he couldn't hardly breath-so never used it. On long drives, we'd have a small litter box made up and open the carrier in a closed car while at a rest stop and see if he'd need to go. Most of the time he didn't. And since it was small amount of litter we'd just throw it away at the rest stop if he did.
At the hotel, we'd set up the bathroom with a bunch of towels on the floor, his litter box, food and water bowls and let him out in the enclosed area.
Mine didn't do well out of the carrier if the car was moving. He'd always try to get under our feet by the pedals.
I'd practice with the cat first, see what type of a traveler he is. Take a few short trips, maybe with someone else in the car too in case it goes bonkers. In the carrier, out of the carrier, maybe a different size carrier if you have one available. Just to see what you are in for.
My vet also told me that it's better to have a health certificate if I was traveing interstate that said the cat had all it's vaccinations up to date. I never needed to use it, but since I'd get the knock out pills from her I got the letter too.
Good luck, you are a very nice mother to attempt this.