Definitely get the Mountain Directory western. No problems with your coach on any of the roads. Coming into the area from the east on the 80 you can take 287 north out of Rawlings to Moran Jct then south into GT, or 191 north to Jackson out of Rock Springs. Both very scenic. Stay at Gros Ventre in Grand Teton. Dry camping with dump and water. Hardly ever fills. In Yellowstone you will need reservations or hit the non reservable ones before 9 AM, they fill that early. (we are camp hosts in Grant and hear the radio calls every day when each CG fills) Grant Village in the south can take a 40 footer, Fishing Bridge, Madison and Canyon all no problem.
Exit the park via the east to Cody. A bit curvy in one area but very doable in your 40' with toad.