That is a rather open-ended question!
I was fortunate enough as a kid to get to take a generally similar trip with my mom, a year and a half after my father passed away. We were tent camping with the periodic motel room. 10 year old me very much enjoyed the trip, and we did get to see many worthwhile things...and, of course, missed many others given the time constraints. Yes, there is a lot of highway time, and having more time would of course be nicer, but if you wait until you can spend months and months making a trip you very well could end up never getting anywhere.
Some highlights (from that trip and other traveling I've done):
- The Corning Glass Museum is well worth visiting (though it may well be practically local to you)
- Niagara falls
- The Henry Ford Museum and Greenfield Village outside of Detroit (two days would not be too much there; the place is huge)
- The Badlands--I really enjoyed that.
- Yellowstone (Huge, one could spend weeks there; also, it was very cold camping in late October when we were there; 6F in the morning in a tent is definitely chilly.)
- CA 1, the Pacific coast highway (depending on your comfort with heights and twisty roads and driving your RV, you may wish to skip that!)
- Hoover dam (take a tour if you go).
- Carlsbad Caverns
- The American Museum of Science and Energy (Oak Ridge, KY) was much better than we anticipated.
- Monticello
- Blue Ridge Parkway/Skyline Drive
I was not so impressed with Mt Rushmore (for me, it's in the category of "yep, now I've seen it" and, for some reason I can't entirely explain, the Grand Canyon. I suspect I'd have a different opinion of the latter now, or with more time to actually explore/hike it.