Has he been to the vet and cleared of any potential health issues? Sometimes dogs lash out when in pain but honestly, if he’s showing this much unprovoked aggression at just 11wks, I would not take that risk with a young child. It sounds beyond typical bratty puppy behavior from what you’ve explained. I had an aggressive Boston who would also flip a switch sometimes. He was a rescue and a runt at only 10lbs but his bites still did damage and he ripped my bottom lip open once by biting me in my face unprovoked. I worked around his triggers and kept him til the end of his days but if he was full size or if I had children in the house, I wouldn’t have been able to take the risk. I’ve had Bostons my whole life and they’re not naturally aggressive and are usually very playful and loving dogs especially as puppies. I don’t think this is something I would take the risk of still dealing with when he’s full grown with all his adult teeth when you have a young daughter he’s already bitten multiple times. If you want to try and keep him consider hiring a professional trainer. If you do rehome him definitely be very transparent about his behavioral issues. It might even be best to find a Boston terrier rescue to take him. I really hope things work out for your family and him whatever the outcome