I second the suggestions that there is way too much time driving and not enough time enjoying and relaxing.
We're taking six weeks just to see Washington and Oregon (including RT from VA). It will be a long haul out there, but once we're there traveling from place to place will only take 2-3 hours every few days so the maximum amount of time will be spent actually enjoying our time there.
As a rule, we have learned that for every 4 hours the GPS tells you it will take, add at least an additional hour. Then there are unplanned things such as RV trouble, traffic jams, illness, etc. We had a flat tire on our (brand new) trailer last trip in a remote area and it cost us day and we had trouble with our Suburban and that cost us another day.
My recommendation would be to focus on one area - Four Corners Loop plus maybe UT and AZ. Or Four Corners and CO and WY. Don't go all the way to CA. Skip the big cities and focus on places that offer recreation that the whole family can enjoy (hiking, biking, rafting, swimming, animal life and so on). Driving through TX alone is a monumental task. Those western states are so much more vast than the eastern ones.
Plan at least one day a week to just chill and catch up on laundry and chores. KOA's are usually good spots for this because they have things for kids to do while you're busy.
It's great you're seeking advice from us veterans. You can learn from our mistakes!
Re: Carlsbad - it's awesome, but make sure you get tickets for a tour well in advance. All you can see without going on a tour is the Big Room.
A good phone app we've used is AllStays. Also check out rvparkreviews.com.
Reserve as early as possible for state and national parks and if you plan to stay in KOA's, they have a discount card (you have to buy it but it pays for itself). Check out Good Sam and Passport America for savings at private CG's.
Have a great trip!