Well I don't know if I can help you to stop the behavior but I can commiserate with you as I have had this problem also with 2 dogs in the house. My roommate's dog started this barking in the middle of the night too when Duncan came into the house as a second dog. I don't know why unless it has something to do with being part of a "pack" now and they are trying to work out dominance issues....but I do know that it has diminished greatly in the last few weeks. It used to be so bad, I was up 3 or 4 or times a night. (I also have neighbors )
Trying to get them to stop sometimes is so frustrating because they just look at you like, "Don't you get it, you need to do something! I can't stop barking! Something is going on but I don't know what it is or why I'm barking at it!" I'll be keeping my fingers crossed for you and hoping others have some great advice!
PS. Someone one told me that a great way to train a dog the "quiet" command was to teach them to "speak" first. Well Duncan can speak just fine but we're getting nowhere with quiet!!!