We just did this in January when we moved 2400 miles away. I was going to fly but we couldn't as it had to higher than 40 degrees the day of travel at both our departure and arrival cities. With departing out of Chicago, the chances of that happening in January were slim!! LOL So I drove it. My mom also came with me.
We left on a Monday evening and arrived here Thursday evening. Neither of my cats enjoy being in the car. One of them, though, is a very quiet cat and quiet content to just hang out in his carrier. The other one is much more vocal in general and much more high maintenance. She was the one I was really worried about!! LOL The vet gave me some drugs for her. He said they wouldn't knock her out but would calm her relax, which they did mostly (she still cried some). Since my mom was with me, she did a lot of the driving (she's a nervous rider) and I held Marcy in my lap in her carrier, which helped her a lot (she's a mama's girl).
Since we drove, this might not come in handy if you do end up flying but...
Our typical travel day:
First thing in the morning I'd feed them a little dry food plus some water. Then we'd get ready for the day and have breakfast. After we loaded up the car, I'd put each of them into the litterbox one more time (I had a small one with liners in it for easy disposable) and then I'd load them up very last. I always took the food and water away about 45 minutes before we left, so they'd have time for it to go through them. I also gave Marcy her pill 30-40 minutes before we left.
We'd stop around lunch time and, depending on how they were doing, I let them out of their carriers but in the car to "stretch" for a few minutes. Only one day did they have any desire to come out. I also offered them the litterbox. Even if they didn't come out, I did open the cage--they'd both stick their heads out a bit but then retreat. And before my mom would get back into the car or I would get out, they were back in their closed cages--we were VERY careful about this!!! While I had no worries about Ziggy venturing out of the car (he's VERY lazy! LOL), Marcy was a BIG concern. Not only would she venture out but she is also very quick, unlike Ziggy. I would have had NO hope of catching her if she did get out.
We drove until 7ish. When we got to the hotel, I'd take them in first and let them out into the bathroom. I also took their food and litterbox in then. They got canned food each night--I gave them a little when we got to the hotel and the rest before bed. Plus their blanket. I'd set it all up in the bathroom before finishing unloading the car. Then we'd go eat. When we got back, they'd be more relaxed and I'd let them out of the bathroom. I put one blanket in the bathroom and one on the bed I slept on so they'd have something that smelled like home to them. The first night they both slept inside one carrier (LOL!!) but by the last night, they were both on the bed with me.
A few tips that came in handy:
1) The small litterbox with liners came in very handy!! It was an easy way to dispose of the waste and I didn't dirty the actual litterbox, so there was nothing to clean before putting it back in the car with the rest of our luggage.
2) I took a large thermos of water from home. Some cats have sensitive stomachs and drinking water from elsewhere can upset it. Each night of the trip I added a little more ice from the hotel to the thermos so it wasn't a big shock to their system.
3) The soft-sided carrier I held on my lap was great. Because it was soft, she could really lean up against me and "feel" me, which I really think was a comfort for Marcy. She did have a hard-sided cage she rode in when I wasn't holding her in my lap. I know the soft-sided don't offer as much protection as the hard-ones and I worried about that. On the other hand, she literally wouldnt' stop crying (even with the drugs) when she wasn't on my lap. And 2400 miles of her crying was more than my nerves could take!! LOL
4) Definitely take a few blankets or shirts that smell like "home" while you're traveling. In each carrier I put one of my husband's (worn) shirts.
5) While I wasn't worried about either of them going to the restroom in their carrier (they are both pretty picky about where they go), I did put a towel in the bottom of each one plus under the carrier. I also took along laundry detergent tablets in case they DID--that way I'd be able to wash at the hotel.
6) Putting them in the bathroom with the door shut definitely helped them. Like when you bring cats to a new home, confining them to one area helps them to become more confident before venturing out.
7) You might want to consider keeping them in the bathroom while you sleep. The first night we had no problems. But when we got back from breakfast, we coudln't find either of them!! After I had a mini-panic attack, I looked under the beds. They had the wooden platforms on all four sides under the box springs, so we didn't think they could be under the beds. Sure enough! Marcy was on the floor under one bed (in the box platform)--I have NO idea how she coudl have gotten in there!!! And Ziggy found a (tiny!) hole in the liner on the bottom of the box springs and crawled INTO the box springs!!! LOL I had to widen the hole he used to get him out!! After that, I checked for ANY possible hiding spots before letting them out of the bathroom.
8) I asked my vet if he recommended trying to drive for longer stretches of the day to get it over with or make frequent stops. He said that for most cats, the longer stretches are best as they don't usually like to get ouf of their cages at stops anyway. So that was the philosophy we took and will take on future moves.
Good luck!!