I think you can file a claim against the dog owner's home owner's insurance. I know that if the other dog had bitten your child on your property, his Home Owner's Insurance would cover that so it may cover damages to your pet, too.
If your neighbor will not relinquish this info to you, contact a liability attorney to see what you can do. The initial consultation is free, and usually you don't have to pay the attorney until you make a recovery. |