It's hard to hear, and some won't want to believe it, but there are times when there is one person in the family that takes the brunt of others anger.
I have a question, is your girlfriend the one in the family that doesn't play the role assigned to her? For instance, her mother has assigned the other daughters the role of the ones who are joyful and happy (I don't know if they would say so if asked, but that's another story)
It can be that your gf is not "cooperating".
However, I don't believe she should, just for the sake of "getting along" The family/mother will just find another reason to be angry.
The father has his role also, he "yelled at" the mother, but maybe his role does not go so far to permit him to actually do anything.
Hard as it might be for you or her to hear, the best thing might be to let time pass. She's 15 today, but in a few years (I know it seems like a horribly long time now) she'll be 18, or 21, or whatever age she'd move out.....THEN, she's free to live decades and decades all the way until she's a hundred years old enjoying her life.
Maybe things can be worked out with the mother, maybe your gf will have to divorce her.
Here's a really good link I think you should read Biscuit. Please go and read it all.
Below is a quick cut and paste that's included there....do you recognize your gf as being one of them?
The six basic roles
Children growing up in a dysfunctional family have been known to adopt one or more of these six basic roles:
The Good Child (also known as the Hero): a child who assumes the parental role.
The Problem Child or Rebel (also known as the Scapegoat): the child who is blamed for most problems related to the family's dysfunction, in spite of often being the only emotionally stable one in the family.
The Caretaker: the one who takes responsibility for the emotional well-being of the family.
The Lost Child: the inconspicuous, quiet one, whose needs are usually ignored or hidden.
The Mascot: uses comedy to divert attention away from the increasingly dysfunctional family system.
The Mastermind: the opportunist who capitalizes on the other family members' faults in order to get whatever he or she wants. Often the object of appeasement by grown-ups