And why should I have to go to these measures because of a freakin' dog? That is completely insane.
I don't think you understand. You aren't going to these measures for a dog. The dog in the situation is not your problem. Your neighbor is your problem. If all dogs on the face of the earth were banned this a**hole would just have something else that was dangerous or intrusive to your lifestyle. This is just like the 16 year old boys in neighborhoods who drive cars (that look like wannabe fast and furious cars) at 65 mph in residential neghborhoods. The problem isn't the car - it is the person driving it. The dog here doesn't know he is doing anything wrong. He is probably bored out of his mind because his master neglects him - so he keeps himself occupied by trying to escape. The dog in this situation likley isn't even dangerous. I say that will a qualifier in that if the dog fells threatened this all goes out the window, and likley the dog will become dangerous. Your neighbor is the problem - clearly demonstrated by the fact that he could care less his dog is digging into your yard, and you have small children. The person sounds like a complete idiot - sometimes extreme measures are needed to deal with idiots, or sometimes you have to move. I know this sucks, but sometimes life sucks.
Have your lawyer advise them ALL that you will file suit and list the city as "correspondent" in any matter of damage or injury that ensues from that point on..
Get a restraining order..
Then load your gun, take it to the range, and practice, practice, practice..
You have the right to protect yourself and your family, and depending on the state, your property..
If the dog comes through the fence, KILL IT..