Well, after the screaming match yesterday with neighbors who live between us and the dog's family (who live 13 houses up the opposite side of the street), and the fact that I went into the garage last night and started mitigating damage to the car, it looks like all we're going to come out with is the need to someday, replace and repaint the bumper cover (I popped out the huge dent on the driver's side, but it's still a bit deformed, and there's spider cracks in the paint above where the dent was), and to buy a new house in a different neighborhood.
So, I'm not going forward with filing an insurance claim of any form, either with our insurance, or with the neighbor's insurance.
What I will do, is tell the officer today that we aren't going to request compensation, but if his DA wants to press charges for the loose dog that caused property damage, then we will support the City in court, fully.
Now, we get to start looking at houses with a three car garage, but that's a different thread for a different time.
Thanks everyone for the suggestions and help.
You've really helped us out during a difficult time.
BC.