RE: Mountains
I'm not sure where you're leaving but if you take I-80 across into Wyoming, (I just looked at the 'Mountain Directory for Truckers and RVers' - available online for East and West of the country, and it states that your first major 'hill' will be at Telephone Canyon (elevation 8900') east of Laramie, WY. This is a 5-mile westbound descent into Laramie at 4-5%. There are 3 lanes climbing and 2 descending.
I would then advise that you take Hwy 191 at Rock Springs off I-80, into Jackson, WY. It has no big grades. Since Grand Teton Nat'l Park is right next to Yellowstone, try to plan a couple nights in that park, if possible. It's a beauty and altogether different from Yellowstone. In the park are 2 huge 300-site non-reservable campgrounds that will accept both a RV and tents. They rarely fill except on the 3-day holidays. They are Gros Ventre, our favorite, and Colter Bay. They are both dry camping - no electric. They do have a water fill and dump station. There is also a RV park in the Tetons right next door to Colter Bay campground. It's called Colter Bay RV. You could stay there with the RV and the others next door at the campground with their tents if you want electric.
Look on the Yellowstone/Grand Teton official web site for maps. From the Tetons you could head directly north on the park road into Yellowstone. Depending where you are going in Yellowstone, this route will take you to Craig Pass around West Thumb. It is rolling hills with some short sections of 5-6%. It's not a biggie.
Another place in the park is Dunraven Pass south of Tower Juction. The descent northbound in approximately 9 miles of steady descent in the 6% range with curves and some hairpin turns. This information is taken from the 'Mountain Directory'.
Yet another is Sylvan Pass between Fishing Bridge and the east entrance of Yellowstone toward Cody. Westbound from Cody is 5-6% grades of mostly rolling hills with a drop of only 800' elevation. Eastbound toward Cody is a 1500' drop in elevation in 6 miles at 6-7%.
Another route is I-90 and picking up 191 at Bozeman, Montana and taking it to West Yellowstone and the west entrance into the park. There are no highway issues with those 2 highways.
Once you start touring with your RV on the secondary highways you could run into mountain driving. Purchase the 'Mountain Directory' if planning to do so.
Full-Timed for 16 Years
.... Back in S&B Again
Traveled 8 yr in a 40' 2004 Newmar Dutch Star Motorhome
& 8 yr in a 33' Travel Supreme 5th Wheel