I empathize with your friend’s plight. She must be deeply disturbed, disappointed, and feeling betrayed by her mother.
This is a susceptible situation and can cause disastrous outcomes if not carefully handled. Is it necessary for her to tell her father? No, it is not. This also allows the mother to cease her behavior and repent.
The Prophet (Allah bless him and give him peace) said, “Whoever conceals the (hidden) fault of his Muslim brother, Allah Most High will conceal his faults on the Day of Resurrection. Whoever exposes the fault of his Muslim brother, Allah will expose his faults, until (so that) He shames him, due to it, in his (own) house.” [Ibn Majah]
First, she should pray to Allah Most High to help her do something. She should pray the prayer of need and even istikhara about confronting her mother. She can also give sadaqa (charity) to ease her nerves and for the baraka.
She should confront her mother and tell her what she knows. She must ask her to stop. It will be difficult for her to do this, but she must attempt to stop this evil if she can. Doing nothing is akin to accepting it. She must try to incite her embarrassment and guilt to encourage her to stop. If the mother doesn’t listen, she can insist that the parents see a counselor or a third party discuss improving their marriage.
She can also get more involved in her mother’s life by spending time with her, praying, asking to cook, and going to religious classes with her. A strong mother-daughter bond can sometimes bring someone back to their senses.
She should consult a local, reliable scholar on the issue. May Allah Most High strengthen her and reward her for trying to do the right thing, and may Allah reward you for trying to help her.
I hope this helps.
[Ustadha] Shazia Ahmad
Checked and Approved by Shaykh Faraz Rabbani