We toured the place in Mansfield MO last October. Lots and lots of items in the museum next to the house. We pulled the (small) travel trailer into the cemetery in town. Just parked for a while, did not camp in the cemetery of course.
If you're really trying to pack Laura Ingalls Wilder spots into your vacation, you might also want to visit Burr Oak, Iowa. It's just over the Minnesota state line north of Decorah, Iowa. This isn't too far south of I-90 in eastern Minnesota. I've often seen the signs for it but never stopped. The Ingalls moved there to help manage a hotel, which has been renovated and now serves as a museum.
That part of Iowa (NE) is very scenic with lots of interesting things to see, but I don't know if you'd want to use up much time there or not.
In De Smet there are two options for spending a few hours. First, the LIW Historical Society gives tours of the surveyors house and a one room school, and Ma n Pa's house in town, which also has a display about the books. The docents are good storytellers. I recommend seeing the surveyors house and the little school next door. The other tour stops were more interesting for grown ups than for kids. Second is the Ingalls Homestead south of town. With the age of your kids, plan several hours there. It is adjacent to the Ingalls property, has several buildings and offers lots of hands on activities and more good storytelling along the way. It is another excellent look at pioneering in the dakotas. Stay at the cg on site if possible.
Mitchell has a nice Cabelas store, too.
The Badlands are a really nice place to overnight IMO. The NPS visitirs center is a must. Rangers will tell you where to see the bighorn sheep and free roaming buffalo. I would choose the cg in the park. Take time to stroll some of the trails and catch a ranger program.
Sturgis rally is the 6th to the 12th of August this year. You really can't imagine how this has a huge effect on the entire black hills region from the devil's Tower to Wall Drug, and all the way south to Custer and beyond. I've spent too much time to count, in the hills, over the last 18 years, and the rally is a great time to be somewhere else. Ten or fifteen years ago, Custer was quiet during the rally, and the action started at Rapid and headed west toward the WY.line. Now you can be at a campground sixty miles from Sturgis and it's nothing but the deafening roar of Harley motors until 2 AM. I have nothing against the rally and all the good things it brings to the hills, but I would really try to be somewhere else from Saturday Aug. 4th until Sunday the 12th. Have a great trip!
Funny, we've been to the three you are skipping: Walnut Grove, the prairie house in Kansas, and the home in Mansfield where she wrote all the books. Walnut Grove can take up the better part of a day, Mansfield a day, Independence a couple of hours at least. We take school groups there frequently.
Between Minnesota and Kansas, there is a Living History Farm in Des Moines. While not specific to the Ingalls stories, it is one of the best museums I've visited with respect to rural and small town life in the late 19th century. The farms also cover earlier periods, but the town is specific to that period the stories cover.