We took our 2 dogs (Aussie and Cattle Dog) to Alaska - the ultimate road trip! The longest we ever left them was for 7.5 hours in Valdez, while we took a boat tour. Prior to our leaving, we walked their wheels off - they were STILL sound asleep when we returned...LOL! We never crated them and never had any problem, but they never gave us a moment's problem in the "regular" house, either.
Granted, you don't get to hike the trails in a National Park (dogs aren't allowed); and there were probably other compromises we made to bring them along, but the peace of mind knowing our dogs were happy and safely with us far outweighed a missed opportunity or two. On the other hand, I've always believed that an RV could be a tempting target for a thief - but I doubt a thief wants to tackle the RV with a dog growling/barking behind the door. So perhaps my dogs provide protection, too?