I can't imagine that trip. It wears me out just reading about it! :)
You have entirely too long of driving days with only one night at destinations.
First, you can't put on lots of miles per day driving an RV. It's nothing like a car. 300 miles would be tops in my estimation. Get to your RV park around 3pm. Set up. Let the kids swim, etc. Relax and have a cool drink, dinner and call it a day. Everyone will be in a better mood.
San Antonio to Carlsbad Caverns - a long drive. Texas is BIG.
Carlsbad to Tucson and spend one day (extremely hot in Tucson and you're not going to be doing outdoor activities)
Missoula, Montana and a day trip to Glacier (Glacier warrants at least 2-3 days and staying in or near the park)
Moab - 1 night - You have a Jeep and Moab is for Jeeping and Arches & Canyonlands Nat'l Parks....4-5 days minimum
and others.......
Even if your wife shares the driving - and she should, the drivers will be exhausted.
Subjecting the 3 children to those long days is going to be very hard on them and you.
I would highly suggest that you cut the sites in 1/2 and eliminate the big cities. You can't do them justice with a day or two.
The kids would be more satisfied with the national parks but even getting way over to California, Oregon and Washington is too much.
You'll enjoy the trip better and will be much more relaxed if you cut it way back - in my opinion.
We full-timed and traveled constantly for 16 years and still didn't see everything. :)