Forget the museums I suggested -- you can't leave your dogs in the car in this weather

What route are you taking? We took 10 east out of Tucson, then went straight north through New Mexico, and headed east again at Albuquerque. There are many rest stops on this route. Traveling with pets in the heat we only eat fast food in the car because we are afraid to leave the animals in the car when it is so hot. (I know fast food is evil, but this is a trip that you will ever make again with your dogs.) We stopped often at places where we could get the dogs out, and the kids could strech their legs, too.
Be sure to pack water bottles and dishes, toys, etc. for your dogs.
You will most likely be tired and stressed out before you even get in the car. Even if you think kids should never watch TV, get a DVD player for your car and some new DVDs. You can give the thing to charity afterwards if you don't want it, but this is going to be a hard trip for all of you.
We've made many long trips with the kids, but traveling while moving is a much more complicated deal. Do whatever you need to get through this. You can get back to your usually parenting (little or no junk food and TV) later.
I hope I don't sound negitive, but I've been there done that with little kids. You will survive and you will be stronger for the experience. Once you've done this you will know that you can do anything. Your kids will grow up as great travlers that you can take anywhere.
GOOD LUCK!