Are the daughters sinful who sheltered their divorced, elderly, and helpless mother, protecting her from the harm of a father who swore to humiliate her? And are they obligated to cut off visits to the father who shuns them at his own request and refuses reconciliation, while his wife prevents them from reaching him?

You have done well by sheltering your mother and preventing your father from oppressing her. This is an act of filial piety (Birr al-Walidain), which is among the best deeds, for the mother is the most deserving of good companionship and kindness. However, this does not mean neglecting the father's rights, for he has his due.

You must treat him with kindness and visit him unless he requests otherwise for his own benefit. Show him and his wife affection and goodwill, and do not abandon him no matter what happens. Appease him with kind words and good deeds, apologize if he appreciates that, and seek mediation from someone who has influence with him.

Abandoning him will only increase his aversion. Strive to pray for him and treat him with kindness, in accordance with the Almighty’s saying: "Nor can goodness and evil be equal. Repel (evil) with what is better: then will he between whom and thee was hatred become as it were thy friend and intimate!" (Quran 41:34). Remember that you have support from Allah as long as you are kind to him, even if he mistreats you. We also recommend this approach with your siblings.