Welcome aboard the RoadTrip America Forums!
My wife and I have a tradition of taking our two grandsons on RoadTrips. As we found on the
first one, the trick is just to have some kid-sized activities for them each day. Such activities don't need nearly the "wow" factor that adults think is required. As you correctly surmise, national parks are a great source of activities, particularly the Junior Ranger programs at each one. State parks are another often overlooked resource. Almost anything that's simply different from what they experience daily in the Old Pueblo will have enough of a "wow" factor for them. And don't underestimate the joy they'll have in simply being on the road with Grandpa and Grandma.
Now to some specific recommendations. I'm going to assume that you've got five or more days. Otherwise, you should just take the shortest possible route, which is considerably different. In any event, with sufficient time, I'd suggest that you first head northeast out of Tucson going through the Salt River Canyon, visiting Petrified Forest National Park, Canyon de Chelly National Monument, and possibly Monument Valley Navajo Tribal Park, making a quick stop at the Four Corners Marker and a more prolonged visit to Mesa Verde National Park. You could then head north on the Million Dollar Highway through Durango and Silverton and then east on US 50 through Black Canyon of the Gunnison National Park, over Royal Gorge in Caņon City and then out onto the Plains from Pueblo. US-50/US-400 would take you through Dodge City, Greensburg (world's biggest hand-dug well) and Wichita (aviation museums), and then I-35 would get you to Kansas City where I-70 would take you the rest of the way to St. Louis.
By the way, if you're grandparents of a certain age, you can get a lifetime pass that gives entry for you and everyone in your car to all national parks and monuments. Well worth looking into.
AZBuck