How old is Olivia?
Sioux Falls has the Washington Pavilion http://www.washingtonpavilion.org/
it has a great science museum
If you need to walk around a bit, the Falls are not too far from the Pavilion. Really pretty and they've done a lot of upkeep to the park. If you'll be in Sioux Falls for the night, I would suggest taking in the light show that happens after sunset. Bring lawn chairs or blankets.
Mitchell has http://www.mitchellindianvillage.org...me/archeo.html
which is a prehistoric indian village that they are actively uncovering.
I would drive by the Corn Palace in Mitchell. It's a good place to take photos in front of, but there is no need to go inside.
I like to stop on the east side of the Missouri River at Chamberlain at the overlook. Very gorgeous views. If you need to get a few groceries/fresh fruit you can at Al's Oasis, just over the river.
The next big stop would be the Badlands. Bring plenty of water as there isn't any to buy once you are in the area. It can get to be over 100F out there in just the dry rocky landscape. There are nice walking trails that let you have magnificent views that make it hard to believe you are in SD. There is a Prairie Homestead just inside the badlands area. I found it interesting, but a little high priced just to see a dugout and early homesteading house.
If you haven't been to Wall Drug, I think you need to stop. Yes, very touristy, but that's the point. It has a good little bookstore, good (but spendy) food, and beautiful old photos in the back area.
I haven't stopped in Murdo for many years so I can't tell you how the museum is there, but it does have Elvis Presley's motorcycle if you want to see that.
In Rapid City, I really liked the Journey museum. It goes through the history of the Black Hills from the formation of them to the Indians to the Gold Rush. Depending on the age of your daughter, she might like Story Book Island http://www.storybookisland.org/
Or Reptile Gardens http://www.reptilegardens.com/
Mt. Rushmore is fantastic to see. I wouldn't use the free parking. It's a hike. Just pay for the parking and call it good.
Crazy Horse is good to see too.
I like Hot Springs. It has a great indoor pool complex as well as the Mammoth Site. http://www.mammothsite.com/
Jewel Cave and Wind Cave are my favorites.
If you are into hiking you can easily find Bridal Veil Falls and Roughlock Falls on the map and visit them for great views.
If you are coming from Minnesota, you might consider taking the smaller highways and cut through DeSmet SD.
Its all about Laura Ingalls Wilder, if that is an interest for you and your daughter.
If you go that way, then I would also stick to the highways and go to Pierre. Sure, the state capital building is nice to look at, but I doubt the history of it would be all that exciting for you. Instead, the
OAHE DAM VISITOR CENTER would be more interesting as well as the cultural heritage center.
Then I would travel south and get back on I-90. You'll be able to go to the Badlands and Wall Drug after this.
As far as the Indian Reservations go....yes, you can drive through them, but I guess I wouldn't. They tend to be out of the way. The services they can provide as far as places to eat or get gas are scarcer too.
Can you tell I love my state and that I love to plan trips?
PM if you have more questions!