There's Ft. Sumter, the USS Yorktown, aquarium, Magnolia Garden, Cypress Swamps, Charlestown Landing, the beach. There's plenty around Charleston for kids.
As for driving through NC, there are a lot NASCAR grarages in Mooresville, if you want to get off 77 take 85 N, there Lowe's Motor Speedway, and Concord Mills (huge outlet mall), and IKEA. On 77, in town there's Discovery Place, also BofA Stadium, and the Bobctas Arena- both offer tours if your into the sports thing. There's historic Bratonsville in SC before you get to Columbia. There isn't a whole lot to see in downtown Charlotte except lots of cars, and a few tall buildings.