What is the ruling on a divorced woman secretly marrying a married man, with her prior knowledge that announcing the marriage would lead to her losing custody of her children?

A marriage is not lawful unless its conditions are met, such as the guardian (wali) and witnesses. If these conditions are not met, the marriage is not considered valid. However, if the conditions are met, the marriage is valid, and there is no harm in not publicizing it for a benefit or to avert a harm. A married woman loses her right to custody, and it transfers to the next deserving person, such as her mother. It is not permissible for her to resort to deception to gain custody after marriage if there is someone else who deserves it.