A couple of fine points on things, first off for your reference Mo is the abbreviation for Missouri, not Montana which is Mt. (could be an issue trying to make reservations, etc.) Second thing I strongly agree with Judy about trying to make reservation at multiple campgrounds inside Yellowstone due to its size, and rather low speed limits which as I recall max out at about 45 mph, even without animal stoppages. As to the route between Denver and Yellowstone regarding the numbers of miles to plan to drive per day, consider the scenery, as mentioned in my previous reply there are some significant stretches of barren nothingness along some of the routes (296 miles from Laramie to Dubois), and there is also some of the most spectacular scenery I have seen outside a national park along others (Wind river canyon south of Thermopolis).
Here is my suggested routing (or the reverse) for a Denver to Yellowstone Grand Tetons trip with 3 nights spent on the road to and from Denver (it could be done in 2, but I assume you will get a mid day start after picking up the RV, and need to get supplies on day 1 or day 2)
Day 1 get out of Denver, be aware you will have about 70 miles of on/off city scape driving north out of Denver, with a first night destination around Laramie, Wy Options are I-25 then I-80 (longer by all freeway driving), or I-25 then US 287 to Laramie which is more scenic, but still a good road. Overnight options around Laramie include Vedauwoo Campground just off I-80 east of Laramie ($20 per night Forest service campground near the pass east of Laramie, or free boondock camping just past the campground at designated pull offs on the forest service road. Nice off grid campground, close to I-80 (about a mile off the highway), the downside is only 28 first come first serve camp sites in the campground that often fill up around mid-late afternoon. Second option KOA journey park in Laramie (correction looks like it is now a former KOA now called RJourney), this is a basic commercial campground, not a resort by any means, but is in town near stores, etc. There is a Wal-Mart supercenter in Larmie that would be a good one stop shopping option to stock up on groceries and camping supplies (there is also another one in Rawlins if you don't stop in Laramie)
Day 2, this is a long drive day, Larmie to Dubois at about 300 miles, nothing much to see here, lots of open land and scrub brush, some of it more / less scenic than other bits. Rawlins is about the only potential stop along the route, and it is mostly a supply stop town. There is stuff to see and do in Dubois, and the scenery drastically improves just as you get there.
Day 3 Dubois to Grand Tetons / Yellowstone this is self explanatory, other than to say there is some nice scenery along the highway west of Dubois as you cross the pass, the pass is an easy drive through the mountains, nothing to worry about on this one, enjoy the views, and stop at some of the scenic pull outs. Dubois is a small town, last option to get limited supplies before hitting the higher in park prices, just don't expect much grocery selection.
Return loop, leave out the east entrance to Yellowstone heading toward Cody, be aware there is almost no businesses between Yellowstone and Cody 60+ miles away as much of it is national forest.
Night 1 Spend it in Cody there are things worth seeing here, perhaps see a rodeo if they are still running the almost nightly rodeos in September, plan to spend hours at the Bufalo Bill center for the west museum (some people would say days), this is also the nearest real town with supplies to Yellowstone if you decide to reverse the route. There could be an argurement that Cody is worth spending 2 nights in town, I will leave that up to you if you want to prioritize nature / scenery vs cultural stuff ie museum / rodeo
Night 2 Cody to Douglas, Wy, take the route by way of Thermopolis (note the mention above of the spectacular wind river canyon drive just south of Thermopolis). This is a circa 250 mile drive, there may be some small town points of interest along the way, one day I would like to make this drive stopping over 3-4 nights to explore some of these towns. Wy 120 from Cody to Thermopolis is a nice drive, just don't expect to see much outside of the 1 or 2 small towns along the way, no people, no houses, nothing. Douglas is a non specific destination for the night, you could opt for Casper, or push on to Glendo or Wheatland.
Night 3, this is sort of up to you, Douglas to Denver is about 230 miles with numerous options to stop for the night if you want to between Cheyene and Denver, or you can push through and easily do this in 1 day as it is all interstate driving, and mostly relatively flat lands once south of Douglas.
p.s. Denver and Salt Lake City are the 2 big airports in the region, everything else pretty much connects through these 2 with smaller commuter flights.