What is the ruling of Islamic law regarding a father's custody of his daughter after divorcing her foreign mother, given his desire to raise her within his family environment to ensure her upbringing in a sound setting, and the mother's refusal of this?

Prophetic hadiths and the actions of the Companions indicate that the mother has the primary right to custody of a child when the parents separate, unless there is an impediment preventing her. The Messenger of Allah, peace and blessings be upon him, and Abu Bakr and Umar, may Allah be pleased with them both, ruled accordingly. The reason for prioritizing the mother is her ability to nurture, show compassion, and exercise patience. For the mother to have custody, she must meet the conditions of sanity, Islam, chastity, trustworthiness, residence, being free from a foreign husband, and being free from influential diseases. If any of these conditions are not met, her right to custody is forfeited.