Yellowstone is a huge park and I’d suggest staying in the park rather than outside to reduce your travel time. Last trip there I put 400 miles on just driving around in the park. At your TT size you should have a lot of options for campgrounds; a few will be off limits. You will be off the grid if you camp there unless you use the RV storage lot – read Fishing Bridge. Both Yellowstone and the Tetons have only one campground with HU’s. Most cg’s allow generator usage, again a few of the more pristine don’t allow them.
Don’t be concerned about dry camping, you’ll adapt fast. It’s just a matter of being more frugal with your resources. I’ve camped for over 50 years and could count the times I’ve used HU’s on my fingers, or at least my fingers and toes. Considering the size of Yellowstone you could pick an area you want to see and select a cg there. Then to see another area just move to a cg in that area.
If you’re in Yellowstone you’ll likely want to check out Grand Teton, too, it’s directly south and spectacular. If you do that you’ll have to decide how to split your time up. I’d suggest a little more time in Yellowstone only because there’s more variety of scenery. Two weeks is a decent amount of time for the trip but I suspect you’ll find it not enough for everything you want to see and you’ll come back again. Have a great trip. A last thought, stock up on food and such before you get there, nothing is cheap in the parks.