I don't know if you mentioned what state you are located in, but I am in PA and we have the same law that others were talking about. If the animal is a threat to you, your family, your pets and/or your livestock, you may shoot with the intent to kill. Once you have the dog on the ground and dead, you are to call the dog warden and let them know what happened. They will then come out, take a full assessment of the situation and the dog.
I just had a horrible situation today. The neighbors dog got out and came up and killed one of my Olive Egger hens and severly wounded my SQ Gold Laced Wyandotte. I was told my the humane society that I couldn't harm the animal, that someone would be out. However, the dog warden for the county that I live in, showed me the law and informed me that I am lawfully allowed to use deadly force. You should call your local warden and see what they say about the situation and if such a law exists in your area.
And I have to tell you, if my kids were the ones being harrassed, I would have shot it in a heartbeat. Nothing messes with my children, especially something that could deadly.