Really. A baseless threat will put your mother in the role of the victim—and the power of the victim role will let her throw more abuse on you. She will feel entitled to say nasty things.
Getting the restraining order or some similar action that cuts her off is what will free you from the role of the victim. From this place you can take pity on her. You have taken action to eliminate the oppressor. Maybe more will be needed. If you are ever so frustrated as to feel helpless about doing that “more which might be needed” then you are back at victim.
Good luck!
PPS — look up the drama triangle and the corresponding empowerment triangle. Might be useful ;)
And no, this is not an exageration.
Threaten her that she will never she her grandchildren again.
It's not your responsibility to try and help your mother.
The need/willingness for change has to come from her. If she won't even consider that it might be her fault and not yours she is a loss cause.
Until she realize this she is a lost cause and you are doing yourself a disfavor by guilt-tripping over her letting her upset your life.