This sounds like resource guarding and not respecting your authority in the "pack". Many Dobermans, being the velcro critters they are, may want to get possessive of you with other dogs around.

You will need to step up and put him in his place (equal to the other 2 dogs in the household) with you and your husband being equally in charge. I would start by putting him on his own place on the floor level when you are settled on the couch. No furniture. Regarding your mom, one thing I always remember is that a trainer told me "Dogs don't "turn" on their owners/handlers. They are simply reinforcing what they believe is their place in the pack. In other words, if he believes he is in charge and someone tells him what to do, he will "correct" that person for issuing a command. It should be understood that nobody challenges the one(s) in charge. You & husband should be in charge and when he snaps at the other dogs you instantly correct him. Just like having 3 kids, if one keeps bullying the other sibling, the parents step in, they don't just let them take over. When your mom is in charge he should never challenge her either. If he can't be controlled by voice commands then keep a leash on him for a sharp correction if he even gives the other dogs a stink-eye. Also same-sex aggression is a real thing, and evidently more-so in this breed, so as he matures you may have even more problems with him, especially with the male bulldog. Definitely begin some serious training to get a handle on this before he gets much older.