I'm trying to figure out where this wall is going. Inside your house? Into the common space? Somewhere else?
Since the open space is shared, you may need to get permission to erect the wall, or at least have a survey done in order to be sure you aren't encroaching on their property.
Also, have you tried calling the town where you live? There are noise ordinances pretty much everywhere. You have already talked to them (and yes, I know that telling the town isn't going to win you a friendship with them, but that already seems to be shot) to no avail. A wall is all well and good but you're right to be concerned that it might not do the trick. You might want to handle at least a part of the problem from the dog side of things.