You picked some wonderful parks/sites to see/hike/camp. I have been in the areas you are planning on going so I may have some advice.

I did not get a chance to go to Badlands when I was in South Dakota. (Ran out of time) Could kind of see it from the freeway and it looked really cool. Also, you will see lots of signs for a town called, Wall. Looks like it might be a tourist trap but worth investigating to see what's there. Mt. Rushmore is a definite. Saw mountain goats while we were there. The town of Keystone which is near Mt. Rushmore may have some fun things for your kids. Think of putt putt, go karts, and water slides. I thought it was kind of tacky but may be something you might be interested in doing. I would highly recommend Devil's Tower while you are there. A very unique geological structure. Lots of hiking and camping options too. Your family might want to consider stopping in the town of Deadwood as well. It is a true Wild West town with daily mock gunfights. Might be a little cheesy but my family enjoyed it. There is a lot of history there and if you like to gamble there are several small casinos downtown. Also, I didn't get a chance to see the Crazy Horse Monument but wanted to check it out. Wind Cave National Park is in that area too. Haven't been to it either so can't add much about it. The Black Hills are beautiful.

I've been to Little Bighorn National Monument. It is a sobering experience. We had a Native American park ranger who was related to people who fought in the battle. Needless to say, you get a different side to the story we all heard in school. She was in tears when she was telling us what happened there and their side won.

Going to the Sun Road is my favorite drive in America. It is unbelievabley beautiful and can be a bit terrifying. Make sure you don't miss the trail of the cedars while in Glacier. I could literally take up a whole thread on that park alone. Place is awesome!!! I'm extremely jealous you are camping at Flathead Lake. So freakin scenic. Don't forget to try local huckleberries while you are there. They are like crack.

Kalispell is a cool town to visit too.

Once again, too much to talk about in one reply thread about Yellowstone. For quick recommendations, I would check out the Lamar Valley (great for seeing wildlife), mammoth hot springs, Norris geyser basin, Grand Canyon of the Yellowstone, and Old Faithful geyser. The park is HUGE so plan your days and time wisely. So much to see and do there. Since you are so close to Grand Teton NP you have to go there. You will be blown away. There are no foothills to block the striking mountains. Jackson Hole is a must visit too. I could probably go on and on but I hope that helps you out some. You'll have a great trip!