Another route from Grand Canyon would be to go N on US 89, N on US 160 until it meets US 191. Follow that to Moab, UT and Arches NP. Continue N on US 191 to Vernal, UT and Dinosaur Nat. Mon., Flaming Gorge, Rock Springs, WY and on N US 191 to Jackson and Grand Teton NP. Then up the Rockefeller Parkway to Yellowstone.
You might want to get a copy of the Mountain Directory, it really helps you pick routes through the mountains. https://www.mountaindirectory.com/mtnshop/
For example, Teton Pass, between Idaho Falls and Jackson is a very steep (+10%) pass I've driven a number of times but NOT in my RV. Likewise, US 14A in eastern WY, and a number of other routes to be avoided.