Does the marriage of the custodial mother annul her right to custody, according to Sharia and the law?

It is advisable for the wife to be patient with her husband, especially when there are children, unless there is severe abuse. The waiting period (iddah (definition)) for a divorced woman is three menstrual cycles, and for a woman who seeks khul' (divorce at her initiation, often by returning the dower), it is one menstrual cycle. Betrothal is forbidden during the waiting period. The mother has a greater right to custody of the children after separation, unless she remarries, based on the Prophet's (peace and blessings be upon him) saying: "You have more right to him as long as you do not marry." If she remarries, her right is forfeited. The sister asking the question should think carefully before divorce or khul', and choose between her children or remarrying, and seek Allah's guidance (istikharah) in that matter. However, if the country's law dictates that the mother retains custody of the children even if she remarries, this contradicts Islamic law.