Dumb question- why dont you have insurance?
I would talk to them nicely and explain the situation and tell them you’d like to sue being that you know it would not really cause them any monetary loss… and you are not angry at them in any way etc… I hope you want to stay on good terms with them, i mean if your a neighbor it could get uncomfortable.
If they really dont want to cooperate just accept it and daven that Hashem should take care of you. He has his ways of routing money in any direction He sees fit! and its really not worth the fight that could result..
Hatzlacha Rabba