She might have been abused but not by her father (he might have even been the only good person in her life when someone else was bad), or she might not have been abused at all but simply has sexual issues from some other source. Whether or not your hunches are correct, any boyfriend has the right to ask his girlfriend to get counseling if her jealous rages are out of control and not appropriate to the situation. *Are* you flirting with those young girls? If you are, you don't have the right to come on in a superior way and tell her that her reactions are wrong and she needs to see a therapist. But if your communications with them are exactly as they would have been with a male relative or haircutter, and she still gets into rages, then you do have the right to ask her to get some counseling.
magoo, you refer to her as your "new girlfriend". She's not a big part of your life right now, I think I would move on if I were you.
She sounds emotionally disturbed. You will want to continue loving close relationships with your niece and the young women your son is involved with, (your haircutter, not so much).
Sometimes, you have to break free and move on to find more healthy relationships. This woman isn't it. In time, if you stay with her she'll cut you off from your beloved niece and son.
I agree with Annie,
Also You prying into her past whether or not she was sexually abused which You might never know is not really appropriate