The Google map route is pretty good, https://www.google.com/maps/dir/Las+....8791025?hl=en
I-15 to near Provo, UT, then U.S. 189 to I-80, then at Rawlins, WY N on U.S. 287. At WY 220 junction, take 220 past Independence Rock (Oregon Trail) to Casper. Then S I-25 to U.S. 18 to SD 89.
Along the way are many side trips, Chief Crazy Horse is another great mountain carving and it has a great Native American museum. Wind Cave NP, Custer SD State Park has a nice drive though nature trail with bison and donkey herds.
The route described has no real steep mountain passes, a couple on I-80, but they aren't too bad. Near Mt. Rushmore there are a couple of scenic highways that shouldn't be missed but can't be driven in an RV. Use your Toad or rent a car for U.S. 16A between SD 244 (entrance to Mt. Rushmore) and SD 36. Switchbacks, loops, small tunnels that give great views of Mt. Rushmore framed by the tunnels. (traveling from SD 36 to SD 244) Needles Highway, also off SD 244, is a beautiful drive, but in a car, not an RV.