The woman is definitely out of line, especially her encounter with the child, but I don't know if I agree with shooting it the next time you see it. I mean, let me rephrase, I do agree but perhaps you should give the woman a verbal warning. Let her know that in the eyes of the law her pet is no better than your pets(which it isn't) and that you are within your rights to eliminate a threat, including her dog. It's easy to get defensive and angry when you are wrong. I am sure if the woman was sorry and apologetic you would have most likely forgiven her but people don't always act as they should. When I had a dog I loved it to death, and if it did that and someone told me they were going to shoot to kill him if he went back for it again, you bet I would take extreme measures to ensure it didn't happen again. But there's always the possibility she gets extra defensive and extra angry and wants to wage all out war. I agree with the other posters you must be persistent, don't let it go, try and be civil and see if she will let up, if not contact legal help.