For a positive: An RV road trip across America would be "memories untold". You and the kids would love it.
Now the negative (I hate to be the first, but here goes):
If you should find a decent used RV that would hold up for this trip it would be great but the miracle would be being able to sell it when you're finished. Very unlikely to get your money back.
This is a very aggressive trip you have planned and YOU won't have much time to enjoy it. It would be much more enjoyable to see less and spend more time in some of the more awesome spots.
Why go to Disney in CA AND Disney in FLA?
The kids may not have much fun in Vegas so you might want to reconsider that.
Yellowstone/Tetons are an awesome place to spend more than a couple of day.
Yosemite would be good.
Salt Lake not much to see there but the Canyons in Utah are awesome.
Durango/Silverton, CO is nice and you can ride the train. The kids would love that.
Rushmore, Custer State Park, Badlands Y'all would enjoy!
For real enjoyment I would eliminate about half your stops and plan some of them for another time.
I rarely recommend RENTING an RV because it is so expensive but it is better than being stuck with one you don't want after the fun is over and if it breaks down they come and help you out!
Anyway GO and enjoy those kids!
