Are the children entitled to claim their share of the rent from their deceased father's house and shop, as well as death compensation and his post-mortem salary, or does that come after the mother's death? What if the mother and brother refuse, knowing that the father registered half of the house and shop in the mother's name twenty years ago?

It is not permissible to prevent any heir from their right to inheritance, even if the mother is alive, and the mother has no guardianship over her children's money. Whoever prevents an heir is sinful, and must repent and restore the rights. Heirs own their legal share of the father's estate, and that includes their share of the rent from the house or shop if the mother owns a part of it. If a dispute arises, the matter should be referred to the Sharia court, which will rule on the case and compel the heirs to fulfill their rights. Referring the matter to the court is not considered an act of disobedience, even if the mother is the oppressor.