A Class C with a rear corner bed and a front cab over bed is doable. Two adults in the cab over, and two in the rear bed, and convert the dinette to a bed at night for the kids. Biggest issue is having enough SAFE seats and seat belts for everyone. Few Class C's are set up for six, and both of the kids will be required by law in most states to be in car seats. These will be very important issues when you begin looking at RV's
There are smaller rental companies and even individuals that own several motorhomes to rent, but you need the security of a well maintained motorhome and a company that can resolve problems should they arise.
I highly suggest you going on Google Maps (desktop or laptop) and finding some of these locations and using it to determine distances. This will quickly be an eye opener for you. (I say use the windows/browser version as I cannot get the Android version of Google Maps to let me pick to random points to determine distances, but only figures distance from present location to a single point). Also switch from default to satellite view, and also try terrain view. Its an eyeopener. You will be at much higher elevations than you are used to, so breath deeply and take it easy till you get accustomed to the altitude.
Spend some evenings reading up on the national parks on their web sites, and elsewhere, and watch some good Youtube videos of some of these parks to see what it is like to visit them and get an idea of time.
I highly suggest, since we are talking small children, watching Less Junk, More Journey and their National Park videos. They have several playlists of videos and one is of their various National Park visits.
https://www.youtube.com/watch?v=T1tVkUkfkM4&list=PLsbCfw4A0PRpFgUEpkqt6w12XaBt6yxE9Also do not miss out on National Monuments, which are also managed by the National Park Service. There are many of them, and all are well worth seeing. You will see National Parks abbreviated at NP and National Monuments as NM (not to be confused with the US state of New Mexico) when people are discussing them online.
Lots of good online info to allow you to plan a doable trip that will not wear you out. You need at least one day a week to take a break and reset, do laundry, etc. Plan on limiting your trip, there is always another year to come and visit.
Charles
