Is it permissible to pay Zakat from the questioner's money to cover his sister's and aunt's rent and expenses, as well as to help his brother, knowing that the sister and aunt suffer from mental disorders and have inherited money under the questioner's disposal, and that his mother prevents the heirs from disposing of their father's share in a common property?

It is not permissible to pay the rent for an aunt's or sister's accommodation from zakat (definition) if they own what suffices them, and if a judicial interdiction has been placed upon them by a judge's ruling. If the brother is in need and has no son, it is not permissible to give him from zakat because his maintenance is obligatory upon you if you are able. If the mother seizes a portion of the inheritance, she must be reminded and warned of the consequences of injustice, and help should be sought from relatives or righteous people to mediate. Otherwise, the Shariah judge is the arbiter. One must honor and be kind to the mother in all circumstances.