I had the good fortune to be able to travel and see pretty much all of the "must see" list as a kid (many on a long tent camping trip with my mom). IMHO I would drop Rushmore from the "must" list to the "nice" list; it seems to me to be the sort of place you see just to say you've been there. I personally was also somewhat less enthralled with the Grand Canyon, but I think I was very much in the minority about that, and also suspect I might have a different impression now.
I do remember being quite enthralled with climbing around the Badlands. I also very much enjoyed the tour of Hoover Dam. Washington, DC is absolutely worth a visit of several days. I enjoyed both Mammoth Cave and Carlsbad Caverns a lot.
Although I didn't go there as a kid, I think the St Louis City Museum ought to be a must see. I'd probably rank it above Disney, even, though they're quite different.
Alaska would be a trip of a lifetime. Going down CA route 1 over the course of a few days is great if you're comfortable driving it, either with or without the camper. The Kennedy Space Center is a good stop, even with the rather commercialized glitzy veneer they've put over it. (The Apollo exhibit is very well done.)
