We crisscross the country a lot, some ideas based off your current route:
Arthur Bryant's BBQ in Kansas City - Burnt ends started here!
NRA Sporting Arms Museum in Springfield, MO - Located in the flagship Bass Pro Shop, includes guns owned by Eisenhower and Teddy Roosevelt
Cahokia Mounds near St. Louis, MO - World Heritage Site, climb the stairs to the top of Monks Mound with a view of St. Louis and the Gateway Arch at the top.
Black Hills in South Dakota - Too many attractions to list, check nps.gov to see all the National Park sites. Wind Cave and Jewel Cave tours sell out months in advance. You might even be able to get a tour of the Missileman Site if the dates work. Wall Drug is the best attraction in the U.S.
Devil's Tower in WY - Make sure your family has seen the Close Encounters movie before you come here!
Haven't been to the famous Iowa State Fair, but it's in August so you might overlap.
Also haven't been to the National WWI Museum in Kansas City, but that's an option.
@Marshfly makes a good case for Colorado-Utah-Wyoming if you haven't been to those states before.