At my RV driving pace (9 AM to 4 PM, medium speeds, 15 minutes stop every two hours) and just those three destinations, this trip (5700 miles) would be 14 days driving, so for three weeks would allow about a week's worth of sightseeing stops.
One of the problems might be that the routing will take you past other places you might want to stop: Arches and Canyonlands NP, Colorado National Monument, Rocky Mountain NP, to say nothing of all the places you could visit on the Plains and in the Midwest (e.g. the RV Museum in Elkhart, Indianapolis Motor Speedway, Living History Farms, or St Louis Arch).
If you skip the Tombstone experience, you could save about 350 miles and a day of driving. If Tombstone is a "must see" I would route through Nashville, Memphis, Little Rock, and El Paso but that just adds more places on the way that you really should stop and see :(
For only the particular western destinations you list, I would fly to Las Vegas, and rent, because you would not have time to enjoy anything enroute, and the fuel costs alone for moving a C from Rhode Island to Tombstone and back are going to be something like $2700 to $3000. You've then got two weeks for touring, enough the make a loop of the parks in southern Utah and northern Arizona.
I don't usually recommend flying over the middle of the country, because there is a lot to see, crossing it hundreds of times I still find more new and interesting places, but if you won't have the time to stop and the only things you want to see are at the far end of the trip, road tripping becomes quite tedious.