1) I think most people dislike the campgrounds in Estes Park, I suggest looking on the west side of RMNP for a CG
2) I would go south from RMNP and stop at Great Sand Dunes, it will be a big hit with your girls, a day there is plenty. Camping there isn't a bad idea tho since you can see the dunes early and without the thousands of foot prints that will appear later.
3) I'd go west from there and stop at Mesa Verde, make reservations online for a couple of tours. They will be filled up if you wait until you get there. Durango is a possibility if you want to take the train ride. Might make reservations for that too, online.
4) Turn south at Cortez and go to the North Rim of the GCNM which has much smaller crowds and the view is just as good in my view those some will argue about that. It's nice and cool too. If you stay in the park make reservations early. Otherwise you'll camp in Jacob Lake at a FHU CG. But that adds a hour long drive into the park.
5) Head north stops at Pipe Springs NM (an hour or two) and Coral Pink Sands SP might be considered.
6) Do Bryce (nice and cool) and Zion (hotter than hades) next. You'll see all the red rock you want which will make up for skipping Arches.
7) To break up the long drive north you might add Capitol Reef (more red rock) and Dinosaur NM (big hit with the girls).
Make sure to make reservations for Yellowstone as early as you can, you want to stay at Fishing Bridge CG and schedule a week there if it fits in you schedule. You can't see the place in that period but you see a lot of it.
In the Badlands you'll want to look at Rushmore ( an hour or two) and stop at Badlands (daytrip). Stay at Custer (reservations) and a stop at Wall Drugs outside Badlands is worth the stop. It's a tourist trap but a first rate one.
Think about a drive thru of Custer NM going back east, I found it surprisingly interesting.
There are probably 50 small parks and attractions along this path that you can use to break up the drives. Get a good map and look at nps.gov