If this were me... I would do what is necessary to protect my family. You have already contacted your neighbors... the local dog warden etc. Therefore I would take matters into my own hands... but would use something larger than a .22lr. I would use something that would drop them in their tracks (.223, .22-250 etc.). My only deciding factor to determine if the animal is someones pet or a stray would be it it has a collar... otherwise they are open for extermination.