I tried to talk my daughter into doing a similar trip.
MN - I've lived here my whole life and yes winters can be brutal, but during the time you are here it will be beautiful.
The Minnesota State Fair starts August 27th and is a must. Personally I'm not a big fan of shopping and if you aren't either Doug, I'd have the family go when you are working to the Mall of America (MOA). Mill City Museum, exploring the trails at Nicollet Island and the Stone Arch Bridge is scenic and educational. Plus a boat cruise on the Mississippi and through the locks from Boom Island. Bakken Museum would be educational and fun for the kids. A stop at Minnehaha Falls and lunch or dinner at Sea Salt Eatery. A walk through the Minneapolis Sculpture Garden. These are just a few recommendations for the Minneapolis area.
If you have time I'd recommend driving north up 35W to Duluth and Grand Marais. The North Shore is beautiful with lots of state parks to visit. Split Rock Lighthouse and Gooseberry Falls are two of my favorites.
In addition here is link of another families 13 month Odyssey of visiting all 50 states trip across America, all 50 states, thosePics
Let me know if you have any questions about my great state