You will have no problem with your 33' MH and toad so don't worry about those gorgeous mountains.
🙂One thing you might want to purchase is the 'Mountain Directory for RVers and Truckers'. It will give you a heads up on the most popular mountain highways.
http://www.mountaindirectory.com/On downhills just remember to be in a lower gear when you start going down, not when you're in the middle and gaining speed. Tap your brakes rather than leaving your foot on them all the time. Going up, just take your time. You'll get there. Perhaps not as fast as you'd like but it'll be o.k.
We love driving secondary highways rather than interstates but to give you a fairly easy route to Dubois I'll suggest some interstate driving. Just remember that some western interstates can have grades of 6-7% (even your I-17 up to Flagstaff) and that's what you'll find on secondary roads, too. So don't be afraid of secondary roads. They are more relaxing to us as you don't have the fast traffic and the truckers pushing you along.
So..to get your started take I-17 north to Flagstaff then 89 north to Page, AZ and on to Panguitch, Utah and continue on 89 to I-70 west to I-15 north through Salt Lake City. Then pick up I-80 east to Rock Springs, Wyoming. Pick up 191 to 28 to 287 through Lander, WY and 26/287 to Dubois.
There are no 'huge' mountains on this route but you'll have some grades. By the time you get to Dubois you'll be a pro so touring Grand Teton Nat'l Park and into Yellowstone will be a piece of cake.
If you can, allow plenty of time for the trip and visit some places along the way. Don't try to drive day after day. That is tiresome. Stop for a couple nights and explore and relax. As retired full-timers we usually got started about 9am and stopped by 2-3pm - no more than 6 hours, if that.
Makes sure your tires are in great shape and not too old. Have a roadside service policy and you're good to go, hopefully you won't have to use it.
Sounds like a nice trip. Have fun planning!
Full-Timed for 16 Years
.... Back in S&B Again
Traveled 8 yr in a 40' 2004 Newmar Dutch Star Motorhome
& 8 yr in a 33' Travel Supreme 5th Wheel