We did this trip last summer & it definitely ranks as one of our favorite vacations ever. Corn Palace & Wall Drug... I agree with others that those are 1 hour stops (max).
I would strongly suggest Ingalls Homestead in DeSmet, which is about 30 mins north of Mitchell, SD (where Corn Palace is). We camped at the Homestead overnight, but you can stay in a wagon or cabin, or visit just for the day. My kids (then 11 &8) had read the Little House Books and the Homestead made the details from those books absolutely come alive.
We spend probably a half day in the Badlands. We did some hiking & got some great pictures.
Once we got to the Black Hills/Mt. Rushmore area, we spent several days in Custer State Park, driving the different loops & we did the Chuckwagon Dinner at the Blue Bell Lodge (it was great).
We spent a half day and then one evening of our trip at Mt. Rushmore. At all of the National Park Sites (and there are many in that area), we did the Jr. Ranger Programs & my kids earned badges- free souvenirs!
I didn't see this on your list, but check into Wind Cave & Jewel Cave National Parks. We did cave tours at both places...our favorite was the lantern tour at Jewel Cave.
We planned this trip last year with the intention of spending 2-3 days at Mt. Rushmore, then 7-8 days at Yellowstone. We found so much to do in the Black Hills area that we decided to save Yellowstone for another trip.
Feel free to ask any questions...I had a hard time finding info last year when we were planning the trip, so I am glad to help.
Jennifer