If you could only do one thing.....

Haven't traveled much in AZ, but I love the Chiricahuas, especially for those interested in birds. An amazing place, but I'm not sure what it's like now, my understanding is that the areas up around Rustler burned pretty bad a few years back. In NM, Pecos Wilderness, hands down, though I also love the Gila. CO, I love the Pagosa Springs area, but you'll get much better advice from some of the locals on this board. WY, the Winds. I've only car-camped in Montana, but if anyone in the family fishes, the Gallatin outside of Bozeman is pretty unbelievable.

RMNP is one of the possibilities. I'm not sure we'll make it to AZ. It'll depend on how we are on time. That may be a trip for the next year. Yellowstone is just one of those bucket list places, and specifically requested by my son.
Glacier NP is also one I'd love to go to. I've got to keep it fairly easy for them. This will be their first time out, so they'll mostly be day hikes. So many places, so little time. I'd love to take the whole summer off to do everything. But I'm keeping it all on a list for future trips.

Depends on what you're looking for. If you love rugged terrain, off-trail travel, and solitude, then the place to go in Colorado is the Gore Range.

I agree with Trinity on the Pecos in NM. Specifically, the area around the Truchas Lakes/Peaks.

Glacier is probably the scenic climax of Montana, but I'd say the Beartooths are the best BPing in the state.

Like Trinity, I generally avoid the NPs for BPing trips--I'm not a fan of the crowds and the permits, although I had a fantastic and relatively crowd-free trip this past summer in North Cascades NP: a place that gets a pass from me because it is near and dear to my heart, and generally not so crowded that you can't find solitude (a couple days from the trailhead, anyway).

Sounds like your son has earmarked Yellowstone. My recommendation is to avoid the "been there, done that" syndrome that is very common in Yellowstone. Dwell time in a fixed location often results in a higher level of appreciation. Toss in Jer's Absaroka-Beartooth recommendation and you have a lot of exploring potential. Also Grand Teton NP is just down the street. The lad wanting Yellowstone pretty much narrows it down to Montana and Wyoming.

My number one Yellowstone suggestion: On the day prior, go to the ranger station at Old Faithful and get a copy of the estimated eruptions times of Old Faithful and the other geysers in the Upper Geyser Basin. Start the following day timed to coincide with the first light eruption of Old Faithful and proceed to the Upper Geyser Basin based on the rough-cut eruption schedule. The first in the AM start will significantly enhance the aesthetic appeal and ambience.

Good luck and best wishes for a great trip.

I really appreciate all the suggestions. My kids are enjoying looking up some of the places online to see what they look like and plan the trip a little better.

Instead of doing one thing in each state, I would pick a single state and do a few things in that state.