I'm not sure who actually owns the park's assets, but it is run as a dual partnership between HFEC and the Dollywood Company. The Dollywood Company represents Dolly's interests in all of her attractions.
Dolly herself probably doesn't actually own any actual piece of the park, and her involvement on the park is purely to support her own brand recognition as well as publicity for the park. I don't even know if she owns all of the Dollywood Company, as it is apparently a subsidiary of HFEC as well.