There are a couple or a few folks on here who take their TTs off road. But I think the TTs are pretty small ones. Like Prof. Dan's Fun Finder, for example... something like 17' long, I think? You really need a short trailer to avoid bottoming out the rear end when going through swales and gullies. And the TT needs to be well built to take the pounding.
Yellowstone is pretty crowded. If I were you, I'd consider staying near the Tetons, maybe at one of the more remote NF possibilities (either boondock or CG), and drive into Yellowstone for a day or two. If I could put up with it that much.
There are all sorts of campers. Some expect the Ritz at the CG. Others don't mind if they do roll through some ruts or block up one side of the RV. I don't know if we can put a "TT culture" label onto TT owners as a whole.
I have to ask, what's the big deal about setting up/taking down a popup, or even loading/unloading a boat, when you have 2 teenagers to do the work for you? ;) Maybe you're looking at this all wrong... you will have free labor! And if it turns out (as some believe) that they will short-circuit your family camping plans, you will have saved some big bucks by using what you have. But on the other hand, if you are thinking that most of your trips will be minus the teens and you want something that will let you (emphasis on 'you') get out there much more often, then you don't need a large TT; shop for a small TT to use for the personal trips, and keep the popup (with the sleeping space) for the family trips. Or a small TT plus a tent for the kiddos... teens like to be by themselves at times.
