You just answered with the suggestion I was about to make, so you’re in good shape already. I have moved several times with Spockie, and once with Sammy as a baby. First, the 2 hours is not going to be any worse than an hour. Be sure to take bottled water to refill fresh water dishes for a drink on a break, or have a hanging water bottle available to them while riding if possible. Use a fleece, litter, hay or a towel on the bottom for comfort and to soak up any loose water or pee accidents. Give them hay and pellets, or a carrot to munch while riding. But basically, if it’s comfortable to meatloaf in the carrier for the duration of the ride, with temperatures in the car being not too hot or cold, they will settle until bumps and turns in the road jostle them.

Once in the house, definitely set up their habitat in the same way that they are used to it. I would pick the room they are going into, set them up, give them lots of fresh food, litter, water and treats, and then close them into the quiet room while you do the rest of the move behind a closed door. The less they see and hear of moving chaos, the better the transition. Leave the things going into their room for last, or get it all done first and then do the rest. You can figure this out by placing their stuff in last on your truck, van, or car. The most familiarity and least commotion as possible and then let them hang out for the rest of the day there. They don’t have to be let out that night, but if you want them to exercise, make sure their room is safe (no wires) and only let them explore that room first for safety. They will explore at their own pace – don’t be surprised if they move out tentatively, go back to the cage, move back out again, go back, etc. A bunny will return to the burrow to make sure all is well as they explore in ever-widening circles.

Your furniture will all be familiar to them too, so they may explore more freely when they realize that only the walls have changed, but the stuff is still the same.
Good luck!

P.S. I’ve move a LOT, and you want a designated resting room for yourself as well. That means move into one room and set it up comfortably, usually a bedroom or den, where you don’t allow a pile of boxes and crap all around. Keep it clean and move into that room from outside of it – unpacking stuff directly into the room. It is a place for you to relax from all the work. It may be good to make that the room where the bunnies are, especially if your TV or computer go in there with them like mine does. That way, when you go to relax and rest, you are keeping them company as well.

My buns have gone on car rides for 7+ hours and they’re fine. Two hours really isn’t long at all. I wouldn’t even worry too much about food or water. Most bunnies don’t drink all that much and most sleep for many hours through the day without needing food or water. You can offer it, but I wouldn’t put it in the carrier or it’ll just make a mess.

Once you get to the new house, set up their area first and just let them relax. They’ll probably be nervous, but they’ll be fine.

I just did 8 hours with 6 buns today, they did fine. Just take breaks for pets and water. I did a 20 minute break every 2.5 hours so they could have some non-moving floor time

ditto that! my bun travels a lot with us back and forth to camp, etc.  and now I think she is unphased. You should be fine!