Have to agree with ulvik, just get off at exit 407, that's Rt. 66/441, and go south to Wears Valley road (rt.321). Construction is done on the road and there are no underpasses/overpasses to deal with, its 3 lanes wide all the way to your campground. Locally the road is named Winnfield-Dunn parkway (441) so there is no parkway that goes around it, that's the road.
The issue will be traffic and how heavy it is, depending on arrival day and even time of day. It will be some 12 miles from the exit on I-40 to Wears Valley road and patience may be in order. I have seen many accidents because of following too closely, especially when towing. Expect it to be bumper to bumper and if it isn't consider it a bonus.
Enjoy your stay in our little part of paradise. If you have any other q's just ask.