A few thoughts:
1 - I've lived in the country and in the city. I've had outdoor cats and (have) indoor cats. My current cats have, minus trips to the vets and one 10 minute escape, been outside a total of about 2 hours in their 8 year lives.
2 - diet food. Nuff said.
3 - Neighbors where I grew up had two dogs they let run loose. Over the years the dogs killed our rabbits, chickens, and a neighbor's geese. We're pretty sure they were also running deer, which is illegal in New Hampshire. This escalated until another neighbor's three-year old German Shepherd was found dead in our field.
A week later, someone shot both dogs.
No one but the owners were sorry.
4 - I think you're obviously on the right track. The woman is housing feral animals. She has a blatant disregard for their health, wellbeing, and actions. She takes no responsibility for their actions, and thus, IMO, forfeits any right to their possesion. "cats will be cats" is exactly the same arguement our dog-owning neighbor used (except it was "dogs will be dogs", of course). You are not responsible for the health and care of her animals. Spend $30 and get your own trap. If the local shelter charges for strays, drop them off at night (ordinarily, I would NEVER recommend this), and make lots of donations at Christmas to make up for it. PHOTOGRAPH EVERYTHING! My wife and I just spent $700 for a digital camera -- best money I may have ever spent. Unlimited pictures, almost no ongoing cost. Photo her basement window, cats, cat waste, damage -- if possible, get testimonial from animal control, health officers, and anyone else official.
And then, if you really wanna play hardball, sue her.
5 - On a lighter, fantasy note -- I've got a dog that comes with a no-cat-comes-back guarantee (my cats survive by moving slow -- really.) She doesn't bark, she doesn't growl, she doesn't warn - she goes from 0 to 60 in the shake of a cat's tail, and can scale a 6' fence - which ain't bad for a dog that only stands 18" at the shoulder.