You can certainly take 20 to 26 in Idaho Falls to the Gros Ventre CG from Henry’s Lake SP but I think that just off the top of my head would be about twice the miles.
DO NOT take your RV on ID 33 from Victor to WY 22 to Jackson! It will take you over TetonPass (8429’), 10% for about 5 miles with a couple of 25-30 MPH turns thrown in just for the pucker factor, that is for EACH direction! (OK solo) BTW excellent view of the lower end of Jackson Hole from the top and in Victor the mercantile (drug Store) makes excellent Huckleberry Shakes!
You can prolly save 10/15 miles when you get to Rigby, ID (the north, first exit thru town to ID 48) then east to Rire, ID and pick up 26 there.
Most of that way to Swan Valley will be thru farm land, in Swan Vally stop at the Rainy Creek store and get a Square Ice Cream (the dippers are square, the cone is round, obviously square hand dipped Ice Cream is better, ask them about why the Square Dippers) Cone.
From there it is thru the mountains, alongside the Snake River/Palisades Res. To Alpine, WY then in the Snake River Canyon (the River will be on your right watch for River rafts, there are turnouts/boat launching areas also to observe the happenings. Watch the traffic circle at Hoback junction (confusing to me) then to Jackson (with the RV take the truck route to by- pass the town square) then to the Gros Ventre CG.
Making a day trip from Jackson, Teton Pass, Victor, (drive a few miles north from Victor for views of the Tetons from the west) Swan Valley, Palisades Res. Snake River etc would be OK!
Or- We would recommend just leaving Henry’s Lake SP early in the AM, Madison, Old Faithful and West Thumb and go thru the park (spectacular scenery) Just follow 89/191. Unless they have changed the rules your unexpired YSNP Pass is good in GTNP.
PM me for any additional information!
2017 GMC 3500 4x4 Denali Duramax
2019 Outdoor RV (ORV) Timber Ridge 24RKS