Branson, MO? I don't know how many children's shows they would have but there are nice paddling rivers and lakes in the southern Missouri Ozarks - also in Arkansas.
Texas Hill Country has nice areas and state parks.
These are some good suggestions from 2gypsies, considering the places you have already been and that you are not necessarily looking for beaches.
There are several possibilities for such a trip. Your first 300 miles would bring you to the Kentucky Horse Park just north of Lexington. The kids would enjoy visiting the Blue Grass for a couple of days.
Then, assuming you are going on to Branson, you could make a stop around Land Between the Lakes in western Kentucky. The Kentucky Parkway system makes that a great drive. There are many great parks in that area. We last stayed at Hurricane Creek COE, but Kentucky has two Resort type state parks in the area.
I am deliberately suggesting this route, avoiding both Nashville and Memphis. If you are heading to Branson they are just traffic problems to avoid.
The entire trip from Michigan to Branson is less than 900 miles.
Another variation would be the Little Rock/Hot Springs area. That could be the destination rather than Branson or it could be an extension. Many great parks in that area. We are planning a trip next week that will include a stop in Maumelle COE near Little Rock and Lake Catherine near Hot Springs. Staying at Lake Catherine would allow easy access to all the attractions of both Little Rock and Hot Springs.
And . . . Spring would be a great time to visit East Texas and the Hill Country. In April the wildflowers would be blooming, the Azaleas and Dogwood Trees in East Texas and the Bluebonnets in the Hill Country. But the kids might not be so interested in natural beauty!
I think my first choice for a family with kids of the age of yours would be the Little Rock/Hot Springs area because you can get a campground on the lake with boating (maybe even swimming if the weather is warm) and great trails, but access to attractions in the nearby towns for day trips. Think about Lake Catherine or Maumelle, but you'd have to make reservations.
And, I would still avoid Nashville and Memphis and take the Western Kentucky/Eastern Arkansas route. I'll be glad to answer any questions about that route as we have made it many times and know the roadways and the campsites along the way.