Use the links in my sig to see what we did with 6 weeks in the Southwest. Leave off the RMNP part of our trip and it would have still been amazing and fit in your time schedule.
I agree with all others in leaving Yellowstone off of this list. We've done a few of these trips now and are gradually migrating to less driving and more getting to know a place.
You will find that in several locations you are leaving long before you'd like to. Especially for an active family.
Regarding summer heat. We did it. Not ideal, but the heat can be planned around. Like others said, the nights cool down enough.
On your list, I'd take off Yellowstone and add Capitol Reef, Arches, Canyonlands and then hit highlights in Colorado on my way for wife to fly out of Denver.
Yellowstone is a place where fast pace doesn't serve well.