This is a very full itinerary for 2 weeks. Maybe 3 weeks. But no way would I try to do this in 2 weeks with young kids. I don't think anyone will have any fun.
Sorry.
I lived in SoCal on and off for a number of years. How are you getting from LAX to all the other places on your list prior to the RV?
None of the places you've got listed are particularly close together and I think you'll find some are repetitive.
I'd pick one theme park. If it's Disney then it's Disney. If it's Universal Studios then it's Universal Studios. Based on the rest of your trip, I'd eliminate Santa Barbara & Universal Studios and do Disney/Huntington Beach. Or Disney/some other OC beach - there are a ton of nice beach towns in Orange County.
You could easily spend several days in San Diego. It's a fantastic city and there are tons of things to do with kids. You might consider Disney and then heading to Carlsbad for Legoland - Carlsbad is also an awesome beach town and family friendly. It's about 1/2 way between Disney & San Diego.
There's a train service along the coast to San Diego too that might be fun - although I'm not exactly sure where it stops in San Diego in relation to the Zoo, Sea World and the other attractions - consider the USS Midway aircraft carrier too. amtrakcalifornia.com/routes/pacific-surfliner
If you're going to Palm Springs (great town), you're virtually next door to Joshua Tree (I lived there twice). It's approximately a 3 hour drive from San Diego to Palm Springs.
I'm not sure why you're getting an RV? With perhaps the exception of Death Valley (again, you might want to reconsider the number of deserts you're visiting and I LIKE the desert) all the places you're going have easy access to clean, reliable family friendly hotels. If you decide to stay in or around Joshua Tree let me know and I can help you out with ideas.
I'd seriously consider doing a straight line route and price out the difference in flying into LAX and out of Las Vegas.
I realize it's a lot to take in and you want to see and do as much as you can but I wouldn't enjoy the trip as you currently have it and I'm afraid you'll spend A LOT of time in a vehicle.