You said you wanted to go West Yellowstone to Jackson, WY.
The easiest and shortest is driving through Yellowstone and through Grand Teton Nat'l Park to Jackson. That's what I'd do.
Your proposed route is o.k. except DO NOT get on 22 at Victor. It's very steep and winding.
Instead, take 33 to Victor then 31 to Swan Valley on Hwy 26. Take Hwy 26 east to Hoback Jct. and then north on 89 to Jackson. This is a good route for a big rig.
Leaving Jackson, take 89 south to 191 to Rock Springs.
Full-timed for 16 Years
. . . Back in S&B Again
Traveled in a 2004 Newmar Dutch Star 40' Diesel