I'm sorry to hear that you are going through this, and it seems so wrong that you are the one to suffer for your neighbors' unwillingness to control their dog. However, as hard as it is, finding a new home for your ducks, may be better in the long run. Since your neighbors are not controlling their dog, there is a real risk, if you keep your ducks, that he may dig under the fence and attack them. Then all the "legal rights" in the world will not matter, your babies will be dead. To protect them is your first priority. Do they have a secure, dog proof run in your yard, or do you let them loose in the yard? You can not change your neighbors behavior, unfortunately, so you may need to make a hard choice, for your babies. You say that the ducks are only 6 weeks old, and this has been going on for a couple of weeks already. You have up to 20 years with your ducks, if you are able to keep them, are you up for a constant battle? Because with neighbors like those, it sounds like they will come up with excuse after excuse to complain about the ducks, the dog BS is just the opening salvo. That's how people like that win. It sucks, but it's reality. If you can protect your ducks,( also against the raccoons and other predators that are there) within your yard, then it may be worth it. Only you can decide.