When someone is using an ax to break into your home, you should be free to kill them.
California, many are surprised to learn, is not a “duty to retreat” state, though it’s not clear there was any place for the homeowner to retreat to, in this case.
In any event, I think you could make the argument for deadly force at moments in this encounter, given the presence of the infant, the weapon and the attacker’s deranged actions. That said, I’m glad it wasn’t necessary.