STOP Killing the cats!!!! If your grandmas chickens wandered into her neighbors yard you wouldn't want them to kill her chickens would you? Have we tried talking to the neighbor and explaining to her that she is not helping those cats by allowing them to breed like that? And by having so many around unfixed and probably deceased. The state of Ohio use to have a catch fix and release program. I don't know if they still do anymore. But they use to trap them and release them on the prisons property here. Check with your state. In the mean time get a dog or electric fence! And tell grandma next time she sees a cat in her yard get out the water hose they hate being sprayed with water! Or buy her a super soaker squirt gun! Let granny have a blast! and yet another reason not to free range your chickens! Pen them up! Where the cats can't get them! Problem solved nobody loses a life and no fight with the neighbor over her nuisance cats!
Frankly, if Grandma's chickens wandered over into the neighbor's yard and were destroying the neighbor's property - say, eating their prize-winning rose bushes, or even just digging and scratching in the garden - the neighbor would have every right to kill the chickens. Especially if it happened time and again, and the neighbors talked to Grandma about it and she did nothing to prevent it from happening again. Sounds to me like the chickens are penned up pretty well. That many cats probably aren't being fed enough which is why the cats are coming over for chicken dinner.
Killing them isn't the right thing to do... What I would do is get some LIVE traps and set them out in various places around your yard. Bait them with dry or wet cat food. When you catch them either take them to the pound, ask around and see if anybody would adopt them, or let them go some where in a wooded area or far away from chickens and your house. Life is precious so please do not kill any more. Would you like it if someone shot and killed you? Don't think so...
Did you read what OP said about taking them to the pound? It would cost them $12 per cat to get rid of them. OP has already eliminated over 30 cats - multiply that by $12. No one should be expected to shell out that much money for a bunch of stray cats. OP lives 40 miles from the Grandma's house. It's really not practical to be making an 80-mile round trip every day to check the
LIVE traps and would be cruel (and against the law where I live) to leave the cats in the trap for days on end until they could get there. Letting them loose to probably starve to death in a wooded area is a great plan. Maybe they can become someone else's problem instead. No, let's not do that one, either. Really, sometimes a quick, humane death is the kindest thing for an animal that's neglected and probably slowly starving to death anyway. Do the cats "like" it if they're shot and killed? They don't even know what hit them, so they really can't like it or not like it. That's reality.
Also, why would a 90 year old woman have chickens? To me, that is to much for a woman of that age to handle.
If she can feed and water them, it's not too much for her to handle. It probably helps keep her going, and more power to her! My 99-year old grandma still lives on her own and still waters her flowers and sweeps her walk and driveway. (Yes, she sweeps her driveway... it makes her happy.
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OP, I hope you can get your problem solved. Maybe beef up the coop and run a little so the cats can't get in? I would stay away from the poison myself, just to avoid killing an unintended target.
And for those of you who think I'm a cat-hater, you're wrong. We have a very spoiled indoor/outdoor cat (we live far enough away from our neighbors he doesn't go bother them) and some barn cats. But people should not have to deal with multiple strays from the neighbors eating their chickens and probably using the lawn and gardens if there are any as litterboxes.