Is a person considered disobedient to their parents if they oppose their father, who wishes to sell the family home and its plot of land, and insists on moving the family to a remote area in order to financially benefit from selling the apartment they currently inhabit, knowing that obeying the father in this matter will lead to the mother's anger and the displacement of the siblings? Is it permissible to give zakat money to unemployed siblings and to the mother? What is the religious ruling on helping the mother divorce the father?

It is the wife's right that her husband provides her with suitable independent housing, to the best of his ability. If moving to another house would harm the mother and siblings, then obedience to the father in that matter is not obligatory. One must still be dutiful to him and not mistreat him, even if he mistreats them. It is not permissible to give zakat to the mother because her maintenance is obligatory upon the husband, unless he is unable or her husband is unjust, in which case her maintenance becomes obligatory upon you. It is permissible to give zakat to needy siblings, provided they are given full ownership of it. It is better to give them from sources other than zakat if possible. If the father abandons the mother and ceases to provide for her, the mother has the right to seek divorce, and there is no harm in assisting her with that, without mistreating the father.