Well, I Don't Know About Dirt
Welcome aboard the RoadTrip America Forums!
But I do know of one great 'back road' between Salt Lake and the Tetons. It's called US-89. And here's where you'll find the schedule of Rodeos in Idaho
AZBuck
Well, it's better than nothing!
I've been on bits and pieces of 89 before -- actually, now that I look at a map, I took 89 from SLC to the Tetons a couple years ago -- and you're right, it's a fantastic drive!
I'd found that Idaho rodeo page also. Unfortunately, the dates that I'll be in Idaho this year, the only rodeo listed is in Oregon! Figures.