What is the ruling on legal custody of my daughter, who resides in America with her divorced mother, who has remarried, and who is seeking to grant her daughter American citizenship?

If the mother remarries, her custody of her daughter is forfeited. The father has a greater right to custody, according to the preponderant opinion, especially since naturalizing in the nationality of a disbelieving country is not permissible except out of necessity. Therefore, it is recommended to exert effort to take the daughter from her mother to protect her, teach her matters of her religion, and raise her upon the creed and ethics of Islam.