Not sure how much time you are spending on this trip
Based on my experience I would focus on what is called the 4 Corners UT-AZ-CO-NM & save the Yellowstone & Glacier for another trip to include Rocky Mountain National Park & much more. In the 4 corners there is plenty to see and includes most of what you have expressed an interest in seeing and in the Corners a must see is Mesa Verde Ntl Park. M.V. will blow you away and it completely negates anything about Columbus "discovering" America. You can do the Grand Canyon on your way out or on your way back. For Grand Canyon camping I recommend the the North Rim all though the views are more dramatic from the South Rim. Be sure to get off the interstate as much as possible. A must do is the old RT 66 from Kingman AZ to Seligman AZ. It's an earlier America frozen in time. In Seligman you have to stop in and see Angel Delgadillo. Incredible man & incredible story of him and RT 66. I see that N. AZ University is excepting his archives which is great news. I was totally fascinated with his place and himself. Check out his Facebook.
You might be surprised at how much driving & trailering you will be doing. So, keep that in mind in your planning. If your going in true high season Natl Park camping sites could be difficult but not impossible. I would not lock myself into too many reservations. You could be looking at a use it or lose it $$ if you do. Keep it flexible so that if you want to hang around longer at a certain place your not pressured to move on. There are usually private camp grounds just outside the Parks that you can default to. Some are good, some are not but they are a place to hang your hat. Also, on a long trip I would plan to take an occasional break from the camper and check into a hotel/motel if just for a hot shower, a better night's sleep, and maybe even a swim. Be sure your okay with trailering this far on a maiden voyage. Just take it slow and easy. Make sure you have the right tow vehicle for the TT. I would do a practice camp set up before you head out. This way when you inevitably get to a camp after dark it may not be such a frustrating experience. AND lastly, someone mentioned to take a nice TV ?? FORGET TV! Your 24/7 entertainment is outside your TT not inside. You can watch TV when you get back. Sounds like a great trip an a memorable experience. Focus on this and not seeing more than you should take on in one trip. Trust me it's a fun trip but it's also a tiring one too. Oh Yeah speaking of TV, if you get the Smithsonian Channel check out their Aerial America series. If you catch the shows right or can DVR them they're great previews on what you will see. Sorry to go on and on but this was one of my most favorite trips I ever took.I hope it's the same for you guys