What is your advice to a girl who knows of her mother's infidelity to her father, and fears that her mother is oblivious to obedience to Allah?

Firstly: You must cover your mother and not expose her shortcomings, for the Prophet, peace and blessings be upon him, said: "Do not harm Allah's servants, nor disgrace them, nor seek out their faults. For whoever seeks out the faults of his Muslim brother, Allah will seek out his faults until He exposes him in his own home."

Secondly: You should admonish your mother and remind her of Allah and warn her of His punishment, while supplicating for her guidance.

Thirdly: If she does not desist from the sin, then accompany her during the times she practices it so that she does not dare to commit it.

Fourthly: Your mother's sin does not negate the obligation of honoring her. Allah Almighty said: "But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them but accompany them in [this] world with appropriate kindness."