What is the ruling regarding a man remaining married to a woman who declared her conversion to Islam, then desired to apostatize from it, given the presence of two children between them, and the difficulty of their custody in the wife's country if divorce were to occur?

You must work to prevent this woman's apostasy from Islam by encouraging her to embrace it, explaining its merits, and warning her of the dangers of apostasy. Try to emigrate with her to a Muslim country. If she apostatizes from Islam, the marriage between you will be dissolved. If she returns to Islam within her waiting period ('iddah), she will return to you with the original marriage contract. An apostate woman has no right to custody of her children, and efforts must be made to prevent her from having custody of them and to take them from her. You must strive to reform them, care for them, guide them well, and supplicate for their guidance. We emphasize the danger of residing in lands of disbelief, especially for children.