Nearly ALL highways in Yellowstone are two lane with narrow shoulders. When traveling from West Yellowstone to the south entrance you will cross the continental divide three times but only one is in any way like mountain driving. All are hilly with a few moderate curves. There are LOTS of places to pull off of the road. Depending on what time of year you go, parking your rig at features like Old Faithful and some of the guyser basins would probably be your biggest problem. Old faithful has plenty of parking but most other attractions have very limited parking available and even less for over-sized vehicles. Making the trip in a single day should be no problem depending on how long you spend viewing attractions and the number of "bear jams" you run into (places where traffic can sometimes be backed up for a mile or more due to wildlife on or near the highway.
One OTHER full hook up parking lot is Colter Bay RV Park (located inside the Colter Bay campground). MOst times of year you WILL need reservations for Colter Bay RV Park.
Good luck / Skip