You are likely to get as many variations of answers from therapists as there are therapists. I have a clear and unambiguous approach I will share, but it is highly biased and based on my experience. Please get some other opinions and choose the one that best suits your needs and personality. This suggestion and perspective may just not be for you.
There are three important clues in your story that lends themselves toward my suggestion. The first is the why is called positive deviance. Of all the ongoing belligerence by this person the one clear thing that worked and worked extremely well was when you stood up to her. You met fire with fire, and she stopped. This is an important clue about how to go forward.
Secondly, you mention that you have tried to be rational and that this has not affected you, but then explain how it has directly affected your depressive reaction and ability to concentrate. What I’m suggesting here is that a rational approach doesn’t work. In fact, I’ll go further in saying that this approach is actually part of what is making the problem worse.
Finally, you say that you are being falsely blamed and are victimized by her rage. Accepting this in any form only allows it to continue. This, in addition to my other two points, leads me to my suggestion for hanging the dynamic.
You have stopped having any needs from this person and are now in orbit around their need to be angry, rageful, and blaming. It is time to start making your needs known and be highly proactive, direct and confronting.
When you need time to work and need quiet, I’d let her know straight away before you begin that you need her to be quiet, not other you, or leave the house, while you are working. I’d encourage you to make this a clear need.
Secondly, I’ll also encourage you to respond directly when she is mouthing off, blaming, or being out of control with her rage. Your job is to assert your own needs in the relationship. Tell her every time she is out of mine, belittles you, blames you, or disrespect your needs. She has no boundaries with you except the ones set when you stood up. Stand up for yourself regularly. Become highly assertive with her. It has worked because people like this family member only get their power through intimidation. Once you are no longer intimidated, they fold.
All this having been said there are three typical causes for someone with the kind of profile this family member has. Often there is alcoholism or abuse in their history and programs like AA might be helpful if they would attend. There is also the possibility of certain types of personality disorders that can cause this. Typically, a psychiatrist or clinical psychologist can help with this diagnosis. Finally, there are medical conditions that can be underneath all this and a neurologist may be the best professional to help.
If my suggestion about your speaking up doesn’t work after a month or so I’d suspect it may be one of the other three causes and follow up with those professionals would be in order.
Wishing you patience and peace,
Proof Positive Blog @ PsychCentral