Love Thy Neighbor. Okay..but can I shoot their dog?

I have reached a point. Not THE point, but definitely A point. One of the things that I absolutely LOVE about rural America is, nearest neighbors are usually at least a mile away.
I like my peace. Actually, I require it.

So, what do you do, when the neighbor dogs start coming to visit? Run them off right? Well, what if they belong to someone who has never provided them with a lick of training?
And what if, they kill your chickens. Ruin your herding dog. And encourage your dogs to start running too?
And the neighbor/hoarder, cannot seem to get it into their head, that this is not cute. It is not acceptable. And their irresponsibility has cost their neighbor money, peace, lives, and what used to be a good dog.

"Oh my dog just loves you and can't stay away." Good. That way your dog will be close enough that I will be pretty much guaranteed a good shot.
Why should I care if that would make them sad? I was damned sad and angry watching my kid crying over the bloodfest in the middle of our yard.

What is even more frustrating is, the fact, that neighbor has a rather impressive dog kennel. That they never use.
Neighbor waxes poetic over how wonderful it is to have such great neighbors and they hope we never move away.
Me? I just swear a lot under my breath and at the top of my lungs.

People aren't stupid for the most part. They can just be incredibly self-absorbed.