In that case, even though technically the dog should have been on leash the instant it left your yard, the neighbor was way out of line. If I was you I'd file a complaint with the police. In most places it's illegal to just shoot a dog, especially one that's obviously a pet and that was not behaving in a threatening manner. At the very least they should have done something about the teenager shooting a gun in a residential area. It's bad enough that he unnecessarily shot a dog, what if he'd missed? One of your kids could have been shot.
One thing that could help you through this difficult time is to do positive things, such as trying to get changes to the laws so that this would not happen to someone else, making a memory book about your dog, or donating to your local shelter in your dog's name.