Well, the whole dog injury incident was your family's fault. If someone had their dog run loose on my property and my dog attacked it and then they came to me and asked for payment, I would tell them that they are an idiot and follow it up by having charges pressed. Maybe a fine will teach you to be less reckless.
Also, I seriously doubt that a legitimate noise complaint would be ignored by the police. Even if it were, there are proper channels to go through to get the officers punished as well. Based on the fact that you say you have called animal control and the police several time, it seems like your family is being the pests. The fact that your dad mentioning shooting his dogs speaks towards the legitimacy of this statement.