Wow, it's a good thing this neighbor doesn't live in Michigan. When things from nature end up on your property, they're pretty much your problem.
Here in Michigan we get issues with leaves in the fall. Your neighbor has a couple of huge oak trees. The leaves fall off, many into your yard. Then there is a windy day and all of his leaves blow into your yard. And you, with no oak trees in your yard, are stuck with raking the leaves. Heck, you don't even know if they are from his trees; they could have come from across the street. This is just the way life is.
Life isn't fair. People like the neighbor who make a big issue out of every little annoyance are never going to be happy. What's the silly woman going to do if she ends up with a dead animal in her yard.