Is it permissible to marry off a daughter without her father's authorization if the parents are divorced and the mother has custody of the children?

A girl is not permitted to marry without her father's permission, even if he is separated from her mother. Her marriage is not valid without his permission, based on the Prophet's (peace be upon him) saying: "Any woman who marries without the permission of her guardian, her marriage is invalid, invalid, invalid." This is unless the father loses the eligibility for guardianship, or prevents his daughter from marrying a suitable partner. In such cases, guardianship transfers to others among the guardians, such as the grandfather, brothers, or paternal uncles, or to the judge if there are no agnatic relatives (asabah) or if they prevent the marriage, based on the Prophet's (peace be upon him) saying: "If they dispute, then the ruler is the guardian of him who has no guardian."