First of all, I would call animal control and report the dog at large and destroying your property. You have a case (with witness's) for small claims court. I would file and let her pay for your birds. This may make her decide to take some action on the dog. If this is not an option, the sure fire way to deal with it is to shot the dog. Which is perfectly legal and necessary if it continues to damage your property. Just be sure if you take the final option, the dog is on YOUR property. Deeply sorry for your lose.