I once had a Spencers monitor escape his cage and help himself to some baby Cunningham skinks I had in a flexarium, it annoyed me to the point that I ended up giving him to a mate. In the area where I live there is a 24hr indoor curfew on cats unless housed in a cat enclosure, but this didnt seem to apply to my next door neighbour's cats. I found one in my Blue tongue pit eating a newborn Blotchy, and on closer inspection i realised it had been watching the female give birth to the babies and then eat them. That day I would estimate I lost about 10-15 young from her. I reported this to my neighbour to which her reply was "They are only stupid little lizards, and the cat is only doing what comes naturally". I then reconstructed the wire top on the enclosure to stop the marauding felines but it made no difference, they just sat on top and stressed the crap out of my Blueys. So I trapped all of her cats and took them to the pound. She abused the hell out of me and said she wished they had eaten all of my lizards, so I constructed a new outdoor enclosure for some new additions but I placed some adult Tiger snakes in there. That day she spied me in the yard and asked me what i was putting in there now so I showed her, and again she went ballistic saying what if one gets out or one of her cats climbs on top of the enclosure? To which I replied i hope they do, needless to say she had an enclosure made for her cats and all is now peachy.
But you would never have considered killing the Spencers monitor would you? Which is my point, that's the same situation I'm in, one pet attacking another pet, no matter what species. The spencers was just doing what came naturally to it, just like my cat. The destruction cats cause to our native wildlife is another issue altogether to this one.
Your neighbour sounds like a bitch, glad you finally got her to put the cats in an enclosure.