My cousin does something similar with a family of 4. They fly to Bozeman, Montana and rent a Class C there. They usually do two weeks and visit sites all over the area. I know they visit National Parks as well, but I don't know where they camp. They are considering buying a Class C and leaving it in Bozeman, then fly out and use it throughout the year. They live in the Maryland suburbs of DC.
If it were me, I'd secure the camp site(s) first, then rent the Motorhome. I wouldn't want the worry of whether or not we can get a site or the stress of trying to find one that time of year.
-Michael
