I don't want to comment on depression as it hasn't been established whether has formally been diagnosed and/or what else is going on with her. Being depressed does not mean that one becomes physically or verbally abusive. Frankly, it does not really matter what your wife's diagnosis is. What matters is her abusive behaviour and her reluctance to take steps to *not* abuse her child.

You cannot cajole someone who does not want to get help and who does not take accountability. Your wife is an adult, she knows what she is doing and she knows there is a child involved. That does not stop her. And *that* says it all.

Children need their mother but not when they are scared of their mother or are, in turn, abused by their mother. This is seriously damaging for children.