Sam22,
My family did a similar 3 week cross country from VA south through TX, Vegas, LA, Yosemite, SanFran, Tahoe, Yellowstone, and Mount Rushmore, back through Saint Louis.
It was a great trip. While it was active, we had the best time and got to see the highlights. IT WAS AWESOME. Yes, we will go back to some of these places and spend some longer times hopefully in the future. But for those nay sayers, know it is doable and can be a blast! It was for us. Not for those faint of heart but allowed us to see most of the things we wanted to see.
So, Go for it and have a great time!