I can have a problem with transferred aggression with my guy. He dislikes other dogs, particularly ones that lunge and bark at him when we are out walking. He goes over threshold and I have to be careful to keep my anatomy out of his reach under those circumstances. When I had my two girls, in similar circumstances they would attack each other! When you can't bite the one you want to bite, bite the one you're with! :)
If I pick Perry up when he is comfortable, he will snark and sometimes grab at my hand. He doesn't bite down, however. I usually just ask him if he's sure he wants to do that, and he quits. I don't like to tempt fate, so I try to be diplomatic most of the time.
Based on what we have seen posted in the past and accepted as humane training by some, we are surprised that you did not use an electric shock collar to correct this unwanted behavior.
Now for a more intelligent and serious approach!
In our opinion, there are certainly territorial and pack issues going on. If you have owned multiple dogs or show dogs then you will understand what we are about to post. When one or more of the pack member/s leave the normal area of the house/home then it disrupts or changes the order in the pack. The hierarchy in the pack also changes when the pack member/s return to the home/house as the members will attempt to re-establish their positions within the hierarchy. This can also affect the pack members who never left because they feel the affects of any change and a need to re-assert themselves and their positions.
Is the the Dog that out of control that you have to pick him up? If so maybe there is more of an issue there then you are addressing and maybe picking up that dog when it surfaces and allowing the behavior to continue is just re-enforcement of undesirable behavior. Is your dog on leash when this is happening or is your dog running free?