As much as i hate to say it shooting a dog with a paintball gun IS ANIMAL CRUELTY!!!! But killing the dog is legal.....go figure!! In todays video age i would video tape the dogs in your yard doing what they do. Chasing your kids and animals and take it to the law. tell them that the owners will not do anything to control the dogs and see what they say to do. Also contact animal control and show them the video and see what they say your options are. I hate the SSS method. It causes bad feelings between you and your neighbors but it is your property and you should be able to enjoy it. Sometimes you have to do what you have to do. Good luck!