I’ll throw another alternative route into the mix....... the route from Butte to West Yellowstone is one I got from another member here back in 2016 when we traveled from West Glacier to West Yellowstone, and I’ll talk the route that way; backwards for you.....
West Glacier to Riverfront in Garrison is a good one day drive. The campground is not fancy, but perfectly adequate for an overnight stay, and easy in easy off the interstate and we had a nice pull through. Noise from the interstate and the RR, but again, it’s fine for an overnight.
From Garrison, we got off the interstate and picked up MT2 in Butte.
There is a WalMart you’ll pass by if you need to reprovision. Part of the parking lot looked like a run down RV park, the only one I’ve seen worse was in Page, AZ.
MT2 to MT41 takes you up and over the mountains / continental divide. That part of MT2 is a rural 2 lane road with no traffic, some tight switchbacks, steeper grades, and may not be a comfortable drive in an RV for some. I thought it was awesome.
Pick up MT41 down to Twin Bridges and pick up MT287.
An alternative could be to pick up MT55 in Whitehall and take it down to it’s junction with MT41. You’d take I90 over the divide, and I have no idea with MT55 is like, but it appears to be in the river valley and an easier drive that MT2 section I took and the related part of MT41 to the junction with MT55.
MT41 from the junction with MT55 and MT287 is a beautiful drive along the valley floor passing through the old western town of Nevada City (not much to see there, unless you want to pay $ to see a few old buildings that didn’t look that interesting) until you get to Virginia City which is worth a stop if you have some time. We just found a spot to pull off the side of the road and walked though town and had lunch. Plus a walk up to the famous Boot Hill cemetery.
Coming out of Virginia City is another winding pass with a long straight downgrade into Ennis where you pick up US287.
So that gives you another alternative route, just pick up US287 off I90 near Three Forks (again, we didn’t drive US287 between Ennis and Three Forks).
US287 from Ennis to the junction with US191 just north of West Yellowstone is a beautiful drive along the Madison River valley. And you pass along Earthquake and Heben lakes as well. US191 into West Yellowstone is a short, easy drive.
This entire route was just incredible, easy to do in a day with time to stop at some sights along the way and get lunch as well. So if you are in for a bit of an adventure it’s an alternative to think about, but may not be a comfortable drive for everyone, although some of the alternative considerations I noted may make it a bit easier.