Okay, 3 weeks then.
1) Want to tour a big city? Wilis (Sears) tower? Chicago. But difficult in an RV.
2) Badlands National Park (one night)
3) Minuteman Missle Silo & Control Center National Historic Site (at the entrance to Badlands) (half day) (NEED TO MAKE RESERVATIONS MANY MONTHS IN ADVANCE, ADVISE TO DO IT NOW) CLICK HERE
4) Waldrug (a few hours)
5) Mount Rushmore (half day) (the visitor center consession sells great icecream "cheap" there, all food is affordably family friendly)
6) Custer State Park, lots of buffalo, Needles Highway (next to Mount Rushmore) (half day)
7) Wind or Jewel Cave National Parks (half day)
8) Devils Tower (the movie close Encounters Filmed There) (half day)
9) Get to Yellowstone (too much to advise here)
10 After Yellowstone, be sure to head home south through Grand Teton National Park
11) Jackson WY
All those little stops before Yellowstone is real nice for the kids and parents too. Much variety without killing much time. EXTREMELY EDUCATIONAL. They see desert formations, caves, a nuclear missle in it's silo (no warhead or fuel anymore) the underground control room, cold war history there. Mount Rushmore history is good too.
Be sure to make the kids watch the movie Close Encounters while driving to Devils Tower. The ride is long enough, but get the move started right away. Don't tell them you are heading there. Don't mention Devils Tower anytime during the trip. Let it surprise them.
At your first National Park entrance, buy the annual park pass. It's a lot of money, but if you do as I advise, it will pay for itself and then some. Don't buy it ahead of time because it's good for 12 months starting the month you buy it.