A barking dog, to many people (to include me), is one of the most intolerable things to have to deal with. I grew up with a lady that lived behind me that had dogs that barked all night long, every night for years. I had countless nights without sleep because of it. I think that bred an intolerance in me of barking dogs. So I can, to a certain degree, sympathize with your neighbor’s intolerance of your dog’s barking.
I’m not sure if this has been asked but… Do you know if your dog suffers from separation anxiety? Do you know if your dog whines and barks while you leave for work?
I think when it comes to a person’s peace and quiet and another person’s right to own a pet, the person’s peace and quiet is going to win. No one should have to tolerate another person’s noisy pet. Getting a dog to quit barking is probably one of the hardest things to cure. You really should consider getting some professional help for your dog, even if it’s just a little bit of barking. A little bit of barking is a ton to someone that doesn’t want to put up with it. I know the Dog Whisperer has a lot of segments that deals with barking dogs that may be helpful too. I have two dogs and we work with them on a constant basis to not bark at the littlest noises. It’s almost a losing battle.