I looked on Google Maps to see where this State Park is located, then brought up the satellite imaging. Wow! those campsites are nice, and long!
We just spent a week in Kentucky (a couple weeks ago). We stayed at Boonsborough State Park and Taylorsville Lake State Park. Both parks were unique in their own way. One is South of Cincinnati, OH, the other is South of Louisville. While at each, we spent a lot of time site seeing, driving well marked county roads, and even our Tom Tom guided us from one place to the next.
Even traveling to Taylorsville, we were really surprised how smooth and nice the back (non interstate) roads are in Kentucky are. However, we were NOT prepared how narrow they are. After getting off the main highway, the roads were barely wide enough for a single car. Driving my duly, I even wondered if the roads were wide enough, and I wasn't even towing then.
The road that led us to Taylorsville was just wide enough for truck and trailer. Thank-goodness we never met anyone coming the other direction the entire road. I'm not sure what we would have done. But the scenery was gorgeous!
Roads are curvy and some are sharp turns, but not impossible, even towing a trailer.
Looking at the Google Satellite imaging of the campground there, there are some pretty long trailers in those campsites. If they can get there, you will be able to also!
Good luck! Drive slow, go down hills in lower gears, and enjoy the journey! Don't get into a hurry to get there. Think safety first ... speed is non-mute! Kentucky is beautiful! Enjoy it all.