Sheikh Hânî al-Jubayr, judge at the Jeddah Supreme Court
The strongest opinion held by people of knowledge is that a woman is not to give up custody of her children to get out of an unwanted marriage. Relinquishing her custody of her children cannot be considered as compensation for khul`. The compensation for khul` should be something of a financial nature. Scholars say that whatever can be given as dowry can also be used as compensation for khul`.
However, sometimes exceptions can be made in cases of ignorance or misunderstanding.
The most important factor for the custody of a child is the child’s interests. This is why the right for custody in Islamic Law sometimes belongs to the father, sometimes to the mother, and sometimes to both. The right for custody also varies according to the circumstances of each individual case.
Ibn `Uthaymîn ruled that a woman waiving her right to custody is not a valid form of compensation in a khul` separation. At the same time, he ruled that if the woman waives her right to custody, then her waiver will be irrevocable.
However, if the father is or becomes unsuitable for custody, then the judge still has the jurisdiction to decide what is best for the child. He may award custody to the wife even if she had already given it up.
Source: Islam Today