You can kill the rat king instead of the cat. And I didn't kill the Mountain Men afterwards, but the quest still didn't finish. It seems it's just bugged.
That is the heart breaking thing, I killed the Rat King but once I was "cleaning" the town the cat flipped out and attacked me as I was killing Orcs. I kept on reloading even taking another path through town but then one of the orcs or mountain men kills the cat...
I played some pretty harsh games in the past like Spec Ops: The Line but this cat is the thing that almost has me in tears...
