I'd definitely take it on some shorter trips and up the steepest hills you can find to see how it is mechanically. You'll be doing some hills once you get near Yellowstone. If o.k. - then go for it.
For what you're planning with lots of people, tents and a RV site, it would be best if you stayed in Yellowstone itself. The RV can go into any campground there but Fishing Bridge is the only one with hookups and tents are not allowed because of bear activity.
Here's Yellowstone's official site for lots of information, including campgrounds:
Yellowstone Nat'l Park
