You sure are doing what you can to protect your babies. The thing is if that guy is crazy enough to want to harm your dogs he could easily throw something into your yard.
I walk around my yard before I let Gracie play there. Not because of neighbors but we have cats that sometimes leave dead bodies around. I have to make sure Gracie doesn't get near one of those.
Your neighbor has no right to complain about occasional barking. Most areas only have ordinances for after 10:00 at night concerning noise. The world is getting to be such a strange place!