Cruise America and El Monte are the largest rental companies; they have offices in many locations all over the U.S. and would likely offer you the best choices of rigs and perhaps prices. Moturis and Road Bear are much smaller companies. Family RV is a small "only-in-San Jose" outfit that also sells rigs and has a small service department. I would suggest comparing prices for like RVs, and see what, if any, "perks" one company might offer over another. Also, check out very carefully *where* the pick-up and return locations are; you want convenience and as much flexibility as possible!
The best starting points for national parks are their websites; some examples:
The websites offer just about all the information that any visitor could want; I suggest that you start with the "Plan Your Visit" link at page left of each park's website. The formats of all the parks' websites are the same.
Don't try to do/see too much in one trip, or try to cover too much territory, or drive too long at a time; with four kids, you will need "downtime" for grocery shopping, doing laundry, spur-of-the moment plans changes, traffic or crowd delays, resting, and taking care of whatever else comes up. If you're scheduled too tightly and/or exhausted from long driving days and rushing to see everything on your itinerary, it's not fun! Also, western U.S. "distances" are often eye-openers for folks from the eastern U.S.; what looks like a "do-able" driving stretch on the map is often very different in reality.