Driving cross country with 4 teenagers

My husband thinks I am nuts but I am planning on driving cross country from NJ to CA this summer with my 4 teenage kids in our Honda Odyssey. (They kind of think I am nuts too but are willing to humor their mother because they are good kids.) I want to do Grand Canyon, BRyce, Zion, Arches, Yellowstone, Mt. Rushmore, Grand Tetons, Badlands, and Mammoth Cave, among other places. We already have a reservation to stay in Grand Canyon for July 7, but no other reservations yet. We will be doing some camping and cheap motels. I have heard that state parks have cabins but I have not had much luck in finding information on them online other than for Dead Horse State Ranch Park.I am planning on leaving June 27 and returning to NJ on July 30. Any advice on the best route or what National Parks to do in what order would be appreciated. Thanks!

The Great American RoadTrip Forum – Planning Summer RoadTrips