That sounds fine
Assume you will be stopping for a break at some time. If she's asleep just leave her in the pet carrier on the car seat while you go into the service station or whatever. If she's awake you could maybe open the top of the pet carrier and chat to her and give her a stroke (if she can't escape easily and isn't a jumper!). Or not open the top but just reassure her and chat.
One thing I do - I have the pet carrier on my knee during the journey, with a blanket over the top so it's dark and flashes of cars etc and noises are less of an issue. Just a fleece blanket. Or a towel might do. I don't know if it helps but I think it must be reassuring to sense your presence while they're on your knee and have your familiar scent. I lift the blanket now and then to check the hamster is ok.
When we leave the pet carrier in the car for a short time I leave the blanket over the top. If she tends to sleep while in there it should be fine. Plenty of substrate in the pet carrier - a little house sounds good, cucumber will be fine for that length of time but you could maybe take more in a little plastic box just in case, or take a water bottle and let her have a drink from it if she wants.
I also hide quite a few treats in the substrate and scatter a little bit of food and put a favourite chew in.
The tricky bit when moving is sorting the hamster when leaving and arriving. When we moved (although we didn't move far) I put the hamster in the pet carrier upstairs in te bedroom with the blanket over while all the packing was going on and the bedroom was packed up/cleared last. When it came to doing the bedroom, moved the hamster downstairs to an empty quiet room. All cage contents were bagged up, including all the substrate. And hamster cage was packed last. We put it in the car actually so it didn't get broken.
At the other end, first thing was to again put the hamster in a quiet room where boxes weren't being unloaded. And set up the hamster cage in a quiet room, put everything back in it, pop the hamster in, and leave them to settle for two or three days. Assume there is one room that will be used less and you can keep all the boxes and unpacking elsewhere. He was absolutely fine.
My worry then was moving his cage to a different room when everything was unpacked because the cage wasn't in the best place, but he adapted to that fine after 2 or 3 weeks too.
Main thing is to just put everything back in the cage as it was without cleaning anything.