Sorry for your loss.
I'm not sure why you weren't supervising your doll (in your yard) if you knew the dog was aggressive. (even in his yard caution should be taken)
I honestly don't see why they should pay. It's really sad and I'm really sorry but the facts are the facts "the mutt" (I don't like that term) was in his yard.
I don't mean to be mean or anything but I'm looking at it from another angle.
Don't mean to give you more pain but it should be a lesson learned.
sad one.