I sympathize. In the last decade and a half, Alabama has become overloaded with people who think everything is public. Well, everything except what they own of course.
I have a very unpleasant memory of an idiot hanging his child upside down over the hot wire because it wanted to "pet the big doggy". The mastiff wasn't amused and neither was I. No trespassing signs, hot wire, and electric fence signs have helped. However, what helps the most is having such a raging, screaming, cursing fit when you catch someone that they spread the word you're crazy. People don't want to deal with crazy.