What is the ruling on this marriage to a foreign woman who declared her conversion to Islam before the marriage, then recanted it, and what is the ruling on remaining with her in the hope of her guidance, especially with a daughter present?

If a woman pronounces the two Shahadas and adheres to the outward rituals, then your marriage to her is valid if the pillars and conditions (guardian and witnesses) are met. You must inform her of the meaning of the two Shahadas and their implications, which include sincere devotion to Allah and following the Messenger and submitting to Allah's law. If she is convinced and commits, then it is well and good. Otherwise, you must separate from her due to her apostasy, and she has no right to custody of her daughter due to her lack of Islam. She should be taught by someone who combines knowledge and wisdom, and one should be deliberate when proceeding with marriage.