What should we do regarding our mother's repeated demand that we relinquish our inheritance to our brother, and her threat of ostracization should we not concede, especially given our urgent need for this inheritance to settle our debts?

It is not permissible to prevent an heir from their rightful share except with their willing consent, as this constitutes consuming people's wealth unjustly. Allah has warned those who disobey Him and His Messenger and transgress the limits of inheritance with Hellfire. The Prophet, peace and blessings be upon him, forbade taking a Muslim's property without their willing consent. Preventing women from inheriting is a pre-Islamic custom of the جاهلية, so it is not permissible for the mother to do this or assist in it, and she is not to be obeyed in this matter. Her anger in this case has no effect. The female heirs should be patient and seek their reward from Allah, and they have the right to take the matter to court to claim their rights.