In Sioux Falls - if they like baseball - there is a minor league team there with a GREAT stadium - you can catch a game there!
Mount Rushmore? Talk the walking tour. There is a town - well - several - on the way up the hill - stop and have lunch - browse the shops.
The Devils Tower is about 2 hours from Mount Rushmore - it's in the North East corner of Wyoming (when leaving Mt Rushmore - take US Route 14 (same one you take up) to Interstate 90 west - towards Sundance, Wyoming then north on route 24). There is a KOA campground as well as a National Park campground. You can walk around the base of the Tower - learn it's history and folklore - you can climb the rocks up to a certain point as well. On the way to the Devil's Tower - there is a quaint Bed & Breakfast called "sawin' logs" - they have a laundromat for guests...
There's a lot to do in Rapid City, South Dakota as well as Spearfish and Sturgis, South Dakota.
What to do in the car?
Your kids are old enough - you can do the:
* alphabet game - from license plates and road signs, complete the alphabet IN ORDER.
* the license plate game - ESPECIALLY at Mount Rushmore!! - see how can get the most state plates!
* colors - find as many different colors - in cars and signs...
* I spy - "I spy with my little brown eye a brown figure" or whatever the person sees - the rest have to guess what it is and the "spyer" has to state IN THE CAR or outside the car...
Stop and get out and every 2 hours. It will keep the kids from getting car crazy.
If you have a portable DVD player - use that as well.
Pack an cooler - keep bread, cheese, lunch meat, etc. in that so you don't stop at McDonald's, Wendy's, etc. for lunch. If you are going to stay at hotels - find the ones that have mini-kitchens and make your own breakfasts.
If you wanted to make it a "round trip" - I would go from Kansas City to Denver, go through the Rocky Mountain National Park and go up to Wyoming and over to Sioux Falls, and then home...that's me. More to see and no duplication on the trip!
Don't forget to drive through Badlands National park. Custer State Park. There is Beaver Lake campground near the Badlands National Park. There is also MinuteMen Missle National Historic Site (off State Route 14).
Using a campground is cheaper than a hotel. So if you have the room - camp. KOA campgrounds typically have pools as well as laundromats so you don't have to pack for 11 days. After you are done site seeing for the day? One of you do the laundry and prepare dinner - while the other takes the kids to the pool. Stop at Wal-Marts and purchase things like hamburgers and hotdogs, chips, etc. make sure you buy only what you need or keep the cooler stocked with ice to keep the food store properly.
Have you considered renting an RV for this trip? I don't know the cost of rental - but then you could save money on food and hotels by having your room to go! :) My parents have a motorhome and I love traveling in that!!
Good luck and have fun!! I LOVE LOVE LOVE Wyoming, Colorado and South Dakota!!