Planning a cross country trip from NC to see Yellowstone and Grand Canyon. Have 16+ days, and would like to include Mt. Rushmore, Yellowstone, Grand Teton, Bryce, Zion, and Grand Canyon. I know this is a lot in one trip but w/kids ages 13 and 10 in year-round school this may be only trip west. Plan on driving w/popup camper. Does this Itinerary sound reasonable?

Aug19 (day1) Start drive from NC to Mount Rushmore
Aug20 (day2) Drive
Aug21 (day3) arrive Mount Rushmore- camp O/N
Aug22 (day4) drive to Yellowstone- arrive and camp at Grant Village
(have reservations for 4 nights)
Aug23-25 Yellowstone
Aug26 (day8) drive to Grand Teton- camp 2 nights? (Colter Bay Campground?)
Aug27 (day9) GTNP
Aug28 (day10) drive to Bryce- camp 2 nights? (North Campground?)
Aug29 (day11) Bryce
Aug30 (day12) Zion and drive to Grand Canyon- camp 2 nights? (Mather Campground?)
Aug31 (day13) Grand Canyon (Northern rim)
Sept1 (day 14) Start drive back to NC (I-40)
Sept2 (day 15) Drive
Sept3 (day 16) Arrive home in Raleigh

Kids have a 3 week break and can possibly stretch this trip a day or two if the money holds out. Have budget of $3000. Is this reasonable? Any suggestions? If we add another day or so, where would you recommend?