Two weeks seems like a long time in planning a trip but when you're RV'ing it, it's not. Be flexible and take your time. Don't rush in order to make all your deadlines. We did that on one trip, and DH who was the primary driver, took naps at rest stops while I took care of the dogs and read. With all the fires in the West, be aware of closed roads so you can take alternates.
Keep lots of handy snacks to eat while driving for a quick pick me up, and plenty of beverages on hand. With your Class C, you've got what you need right at hand, but stop to enjoy your meals when en route. Don't be afraid to stop overnight at Cabbela's or Cracker Barrels, just be sure to ask the manager and buy something small as a thank you. Lock up and sleep well, then off on the next day's travel.
Avoid Teton Pass when leaving the Tetons - that's Hwy 22. A better, and safer route is to take 25/89 to Alpine Junction then 89 to Afton, from there you could go 89 into Logan through the Logan canyon, but it's a narrow, rough climb and trucks are advised to go 20mph, so instead from Montpelier take 89 to 30 into Wyoming to Kemmerer then 189 to West I-80 to I-84 then into Salt Lake City.
2011 Bighorn 3055RL, 2011 F350 DRW 6.7L 4x4 Diesel Lariat and Hensley TrailerSaver BD3, 1992 Jeep ZJ and 1978 Coleman Concord Pop-Up for remote camping
Dave & Renee plus (Champ, Molly, Paris, Missy, and Maggie in spirit), Mica, Mabel, and Melton