You might do better with a small/private RV rental company. A lot of dealerships have rentals as well as small rental businesses and people renting their personal RV's. Craigslist usually has some ads. You can get a lot more bang for your buck, a nicer RV and perhaps a Class A for the same price as you would a Class C from a major rental company. Also - typical rental units from large companies are stripped down, no fills rv's and usually pretty worn down. As far as economics - read the fine print. Usually you will have extra fees for mileage, LP, cleaning, tank fees etc. These - especially mileage - can add up fast.
As others have said, plan your trip so you can actually enjoy what you want to see and not spending all your time driving. Find places that have rental cars locally to destinations so you can further explore, etc.
Avoid travelling on US Holidays. Traffic and your destinations will be a jam packed, miserable experience.
Bring media devices and movies etc for the small ones while you travel as well as plenty of snacks etc. There is nothing like hungry young ones that are road weary and need something to entertain them. RV's offer a good way to travel with kids because of this.
Class A's typically provide the most room although not always more sleeping capacity than a C. But many A's now have cab over bunks. Class A's will ride nicer. Class C's probably ride the worst of all RV's (A, B's and C's)
Class B's are more nimble and will provide the best mileage, however they are the smallest and likely won't have the room for your scenario. They are also not really any cheaper than a Class A if you can find one to rent at all.
