I would not personally put any dog down because of these incidents but if Buster gets out into public and fights with another dog on accident or some sort then you may not have a choice after that. So for starters Buster may be uncomfortable in his new living situation, unless Buster has always acted this way even before your son moved in with you. You did a smart thing for hiring a professional and trying to solve the problem. I would consider kenneling Buster which includes putting him in there when people come over and every night to sleep, so you won’t have to wake up at 3am because the dogs are fighting. That’s a little too much. Also kenneling him will allow your family to introduce people without having to worry how Buster will react. Is Buster neutered? If not, that could be a huge factor. If he got neutered late, this could also play a factor in his behavior. I would kennel him and be very consistant in his training! No matter how old Buster is, train train train and exercise.
