A few points for you to consider:
1. I have only met this woman once during the bad snow we had last winter. I did not remember her, and she certainly should have had no expectation of exemption from my No Trespassing signs. I have other neighbors that I socialize with and know well, who definitely have exemption from my No Trespassing signs, but they still call me when they want to come over. I do the same. [I agree]
2. When I talked to the woman, I took her to the side, while the other woman who doesn't even live here took care of both kids. It was a private one-on-one conversaton, and I certainly was not an ass. I was stern, but cordial and respectful, and did not raise my voice.
3. I threatened noone. I do not htreaten people. I react and respond to threats against me. In this case there was no threatening behavior, so there was no force response. I am a former cop and know how to talk to people to get my point across. [I understand you may not of intended to threaten her, but people don't always hear things the way we say them.] [How cops talk is not how neighbors talk]
4. I also want no liability for anything that may happen on my property related to this woman or her kids being there. For example, if one of her kids drowns in my pond or sneaks onto a hot shooting range is not something I want to contemplate. I do not want anyone on my property who doesn't have my permission to be there. I made my point very clear. Also, I do not "hint". I make my points very directly, especially where my rights and my privacy are concerned. [Very reasonable concerns, the fact you use the property for live-fire is definitely something you should mention.]
5. There were no "cuss" words used. I am not sure where you got that. [The :cuss: charecter was used as in 'blah blah blah' because what you say, and what she heard, are different things.]
6. I don't mind being neighborly. In fact, I told her that if she had asked for permission to take some pictures by my pond, I would have gladly given it. Since instead she and her party chose to sneak on my property from the back (based on which motion points were activated), I decided that she did not deserve consideration and needed to leave. [Harsh but reasonable]
7. Anti-social and anti-community, in my opinion, apply to her and not to me. My neighbors caught her previously on their property and were equally stern with her. This was my turn, and I do not believe that she will be back. I usually give people one chance in life, and if they screw up, they are out. She is persona non-grata as far as I am concerned. [You must be a lonely person, as even prophets from God make mistakes. If this is true, that you don't know how to forgive people, you are a hypocrite.]
There is by the way a reason that I live on fenced 20 acres, and not in a subdivision. The main one is that I don't want to deal with stupid people that I have had to deal with before I retired.