when a dog has no problem redirecting his aggression on the human, it becomes a little bit of a dangerous problem. how old is the dog. the dog whether gets to excited that it snaps at the handler unintentionally or it is in such a dominant state that it will correct (bite) the human to let him go to pin down the other dog on the other side of the fence. bothe are dangerous. a dog that becomes so excited that it can no longer think can bite. a dog that is so dominant that it disregards the human as an authority figure can bite to disagree with the human.
point blank is that whatever you are doing isn't working. it might not be so bad now but as time goes by your dog will become very dominant and dangerous to your family. with a dog in this state of mind it is difficult to tell you how to handle it. it seems that you allow him to escalate to such intensity that alot of techniques given will need a skilled handler to adjust to that particular case. A correction will work, but exactly what will the correction involve? what timing? this case...I think...requires a professional to tailor a system that will solve your issue. It is more than just the yapping dogs...it is the overall life that the dog is living that has to be examined.
I suggest finding a professional.
look up International Association of Canine Proffesionals. they have a search engine that can find certified proffessionals in your area/ i think it is
The International Association of Canine Professionals
best of luck