thumb, not sure where you are staying in Vidalia, but I think there is only one park there, so I guess I do know. Have fun and enjoy the sites of Natchez. I think the best part was the horse drawn carriage tour. Driver was an retired gentleman, who did the tours because he loved history and sharing.
Can't tell you how to avoid Baton Rouge, cause that was our next stop. Stayed at the Equestrian Park for several days. Mid week it was great, when I left on Friday, it was beginning to fill up. It is very near LSU campus and stadium, so there were lots of Tigers in the lot.