I would suggest the following but I don't have little ones to find things to do.
Warriors SP-Kingsport,TN in April but not race weekend.
Claboughs-Pigeon Forge,TN in May.
River Plantation-Sevierville,TN in June.
Davy Crockett Birthplace SP-Limestone,TN in July
Smokey Bear-Gatlinburg,TN in August
Claboughs-Pigeon Forge,TN in September
Jellystone-Gatlinburg,TN in October
I probably wouldn't be able to get to all of them but it sure is a nice dream.
Also got to work in the beach sometime during all that.