You'll find every kind and size RVs and trucks touring the West. You may not climb hills fast but you'll get there.
How long do you have for this trip? You have 10 major parks listed (also include Grand Teton Nat'l Park which is right next to Yellowstone). Staying at least 3 days at each park is 30 days. Then there's 4 or more days to drive out and back...that's 38 days. You'll want to stop at more places along the way that you'll see... possibly up to 40 days by now. Do you have the time?