When we moved from San Diego to Michigan, we traveled cross country with two dogs. We also did it in the other direction, two years later, only this time with one.

On the way out to Michigan, we really wanted to take our time and not rush so that we could give the doggies lots of breaks from being in the back of the SUV (an Isuzu Rodeo). We had no trouble getting two dogs into Motel 6's along the way (we never really mentioned that there were two...), and generally had no issues at all.
The only thing that we did find was that we couldn't really do anything but travel and stay in the hotel room with the dogs. We didn't want to leave the dogs in the hotel room alone (and, of course, the hotel doesn't want you to do that either), and there was not really anywhere to go that we could take them with us. Sounds like you guys might be doing some hiking/camping along the way, though, so that sounds doggy inclusive. It should be a good time!