There are some long days in there, for sure, but you probably know better than I do how well you will or will not handle them. It would be very, very helpful if you had more than one driver on some of the long days, even if it's only for an hour or two once or twice during the day. (I would not suggest the eight or ten year old as the backup driver, though. ;))
I'd give myself an extra day between Teddy Roosevelt and Mackinaw; two ten hour plus days back-to-back, especially at the end of the trip when you are somewhat likely to be rather tired already, is quite a bit. Three seven hour days is less stressful.
I would add Hoover Dam (one day, probably not quite a full day); it's a fascinating tour. I would also suggest adding the St Louis City Museum, which is worth a pretty full day if your a child or young at heart.
I'd also suggest not setting the entire itinerary in stone to begin with, but be willing to adjust as you see how things go. Reservations fairly far in advance would be advisable for Yellowstone and maybe a few of the other more popular parks, but much of the rest could likely be done with at most a few days advance reservation, especially if you're a little flexible about what sort of campsites you accept.
Mountain driving mostly means being willing to go at a slower pace up and down, primarily using engine braking on the down side. I'm guessing this is a gas motorhome with a Ford chassis; the tow/haul mode would help a lot going down. With appropriate caution, it's not really that much harder or more challenging than driving on flat ground. (Without appropriate caution, it can of course quickly become deadly--as can any driving, but the margin for error is somewhat smaller especially when descending a grade.)
