You're limited as far as what you are looking for near The Grand Tetons. The best RV park around there is Colter Bay but there are lots of trees, heavily wooded, for both the full hook up and dry campground. There's the Virginian in town but we've driven through to check them out and it's basically a parking lot. There's the Teton Resort RV park, but that's not quite a resort - dirt parking lot and side by side. Flagg Ranch off the Rockefeller Hwy is also heavily wooded with dirt sites. You may have to compromise in that area. Another thought would be to stay on the Idaho side in either Victor or Driggs - check that area out on campground reviews. I know there's a nice little RV park in Driggs with your criteria. There's one in Victor we stayed at but I don't remember a hot tub there.
We visited Glacier two consecutive years and stayed at different RV parks - one was Mountain Meadows - very nice, wooded, no hot tub. Then we stayed at the KOA there, near Hungry Horse. Super nice, both wooded and open meadow sites and they have a hot tub. We used it and enjoyed it, especially late at night with the stars out.
Hope this helps.
