Is it permissible to listen to relatives' stories about their suffering and how others treated them harshly, and about their personal matters, in order to benefit from them in avoiding problems in the future?

A Muslim's disclosure of the injustices they have suffered in their life, whether in the past or present, is not forbidden backbiting (gheebah) nor a slip of the tongue. The wronged person (mazlum) has authority over their oppressor, and Islamic law does not hold them accountable for what they confide about themselves.

Therefore, if your mother's or grandmother's stories about their relatives include instances of injustice, such as beatings, insults, deprivation, usurpation of rights, and bad manners, then there is no harm in their speech or in your listening. This is in accordance with the Almighty's saying: (Allah does not like the public utterance of evil, except by one who has been wronged. And Allah is Hearing and Knowing) [An-Nisa/148]. Jurists have exempted the wronged person from the prohibition of backbiting, permitting them to speak about their oppressor concerning the injustice they suffered, or to supplicate against them, or to warn against them.

However, it is preferable not to name the person being spoken about, keeping their name anonymous, so that lessons and admonitions can be drawn without falling into the backbiting of a specific individual.