Well, you may be sorry you asked for my advice, but I'm hoping it helps. I just moved cross-country with two cats back in May.
Take them to the vet to be sure they're healthy
I did with Bella, and I had a full blood panel drawn so I would have a baseline to compare to after the move, in case she started showing signs of illness. (This, incidentally, helped to diagnose her CRF five months later) Get copies of all your vet records while you're there.
Be sure you have a carrier for each kitty. I can tell you from experience, travelling with kitties loose in the car may sound like fun, but it can
be downright dangerous!
Try to get your kitty used to a figure-8 harness. It'll be easier to control them when you take stretch breaks if you have a leash.
Pack a care kit for the cat(s): food, water, a litterbox (covered ones work best and can be strategically packed for easy access on the road) and some favorite toys, FELIWAY spray, a favorite bed if they have one. Helps 'em feel more at home on the road.
If you have a chance, secure the kittie(s) in one room, with a FELIWAY diffuser and their bedding/toys, while the movers are there, so they don't get trampled underfoot or worse, escape.
Prep the carrier(s) by lining with towels/blankets and spraying them down with Feliway to calm the kitties in transit. Repeat this process every morning if you're on the road for more than one day, and it'll help maintain everyone's sanity.
VERY IMPORTANT!!! Withhold food for at least four hours before travelling. Free feed in the evening when you get to the hotel, but put up the food before bed. Don't worry, Kitty probably won't feel like eating while you're driving anyway.
I learned this the hard way with Bella; she ate breakfast abt 90 mins before we left, and when we got out on the interstate, she was nervous as usual. She yowled non-stop for over an hour, until she literally made herself sick
So after less than two hours on the road, we stopped to clean out the cat carrier and clean her up as best we could.
I found my Bella was calmer when she could see me from inside her carrier (and get the occasional scritch through the bars
). Expect some nerves when you start out, but they should settle in after an hour or so. Mika never made a peep, but she was never the nervous type anyway. Bella was a little tougher, but even she got some shut-eye during the drive.
Give kitty stretch/potty breaks when you do. Attach the leash to the harness so she doesn't bolt, and so she'll be easier to retrieve if she decides to find a hideout (Bella's favorite was to try and climb up in the engine compartment) If you stop at a nicely landscaped rest area, you can both take a stroll in the grass!!! He may be more at home in his own litterbox, so be sure to at least offer it, every 3-4hours usually worked well for us.
Just like with introductions, be sure to confine Kitty to one room to start out. A whole new house can be pretty overwhelming, with all the new sights, sounds and smells. Plug in your Feliway diffuser to calm them. Leave the old blankets, carrier, litterbox and toys in a room that's not high traffic while the movers are there. Give 'em a day or two to get used to the new space, visit them often to let 'em know you still love 'em, and let them explore the new place on their own schedule.
Just be aware that they WILL find new and interesting hiding spaces that you never thought possible.