How about the Jellystone in Natural Bridge? It's about 5 hrs from Dandridge, give or take. I don't know where you are coming from in NJ, but it's about 5 hours from Newark.
Most Jellystone's are so kid-friendly, it's sickening. We stayed at the one in Luray for 3 days with the express reason of seeing Luray Caverns, but never made it out of the campground. The kids had a blast! and there were plenty of them.
2017 Ford F350 Crew Cab 6.7L 4x4 DRW