First, what is the "bad act" of your neighbor? Kids running in your yard, and come into your house to talk to you is not really criminal. Throwing eggs on your house might be problem, but you cannot prove it was them.
Second, even if above allegations are true, I don't think most judge would agree that you are in fear of physical injury.
You can't stop your neighbor from complaining about your renter. Maybe you can erect a fence to stop their children from trespassing. There are many common sense ways to resolve neighbor dispute, and so far I have not seen anything that lawyer can help you.
If you don't agree, tell us more FACTs, get a camera and record more EVIDENCE, not just rehash about the argument you had with your neighbor.