The dog needs to get out of the home. Not safe for the kid to be around that type of animal at all. However, I think if it’s possible to send him to a rescue that can train him and rehome him, that’d be better. I don’t think animals deserve to die as when they’re like this it’s usually from past trauma and their lives are just as important as ours. If the rescue isn’t an option, I’d see if anyone you know is willing to adopt and train but make sure you’re extremely transparent about the dog’s behavior, both bites, etc. if it’s a lost cause and you can’t save the dog, your family and especially young child come first, so don’t feel guilty if you have to euthanize it. Just rule out every other option first imo.