You folks haven't got the farmer stylee yet. Neighbours are not a problem. Just deal with it.
Now, if hens are coming on your land and trashing your stuff then the owner has no reason to complain if the hens don't come back. I'm not going to advocate killing and eating perfectly good layers but to me, if it happens more than a couple times then the hens are yours. You can move them on to someone who will take good care of them. They will soon get tired of their precious layers vanishing. In the countryside, possession in a little more than nine tenths.