We made similar trips in miles and sites when kids were 5 and 8, again 7 and 10, and then finally 12 and 15 years old. Your kids will find fun what they do from a young age. They still love to camp at 15 and 18. Both girls.
As far throw away the plan, it's not feasible using vacation but you should build flexibility. We booked national parks and then winged it on zig zags to see states. We did no more than 2 days hard drive without a stop. Preferred full day drive then half day drive and half site see during transit.
I would not add Rushmore. Biggest disappointment for us and we've been to 48 states.
Given your ambitious schedule, Arches one day and Canyon Lands a second day. Use the other day and a half to see someone on the way and break up the four day drive to the Grand Canyon. You will need that. I don't think you can get to GCNP in four days anyway and I've driven most of that route many times, though only Louisiana to AZ frequently as one trip.
Be willing to flex. A blow out cost us a day at Yellowstone. We couldn't tack on a night camping because of availability but we did stay half a day past our planned departure and flexed later in that trip. Bailed on Rushmore after an hour. If we had planned hikes, maybe it would be different but as part of a larger trip it wasn't worth it. Those aren't on your agenda but you will find places where you need to flex. Know that in advance.
And have fun!