If you want to skip some Interstate stay on 93 to Shoshone and take 26/20 on to W Yellowstone. Decent road. Might consider a stop at Craters of the Moon east of Carey, ID. The visitor center is worth a stop and there is parking for large vehicles. https://www.nps.gov/crmo/index.htm
I-80 to Wells, US 93 to Twin Falls, I-84-I-86-I-15 to Idaho Falls, US 20 to Weat Yellowstone. Piece of cake, decent roads. Ashton thru Island Park into West Yellowstone, a beautiful drive. We use this with a dually crew cab pulling a 40' fifth wheel.