Is the mother entitled to claim the usufruct of the house that the father wrote for her but did not officially register, and what is the ruling on her refusal to distribute the inheritance?

It is not considered an act of disobedience (ʿuqūq) for children to request their share of their father's inheritance. It is preferable to reach a mutual agreement and seek the help of wise individuals to resolve the issue. If no agreement is reached, the matter should be referred to the Sharia court. If a husband grants the usufruct of his house to his wife for life (al-ʿumra), this is legally permissible and is a gift (hiba) that cannot be revoked, and it becomes binding upon possession. However, if this was a will (waṣiyya) to take effect after death, it is not valid for an heir, nor for more than one-third of the estate, unless approved by the other heirs.