WE travel to and from YNP twice a year for the last 25 years.. Coming from Cody I would take the drive over the Big Horn Mtns and down thru the east gate of YNP..
Then cut over on the south loop to West Thumb Junction and turn south heading into Tetons NP... That takes you right into Jackson..
The road from Cody to east entrance is excellent.. Many places to safely pull over crossing the Big Horns to take a stretch and get some nice pics..
Diesel fuel is not an issue... East entrance Fishing Bridge is fuel station and one at West Thumb area as well. the drive coming into the Tetons is nice, lots of places to stop and pull over with a larger RV..
Ive done that drive at least a dozen times... lots to see .. IMO...
I see large Class A units with trailer behind them having zero issues... I pull a 36 foot fifth wheel
one of several maps showing the loop, driving distances from east entrance to south entrance of YNP and a map of the Tetons
https://www.nps.gov/yell/planyourvis...ff_Map2016.pdf