Is it permissible for a divorced woman who has no income and for whom the maintenance is insufficient to marry and leave her children with their father without sin?

A mother is permitted to marry and leave her children with their father. If she is in need of financial support, then marriage is more appropriate. If the only need for marriage is financial support, and the children are young and there is a fear of them being neglected, then it is better for righteous people to mediate with the father to increase the financial support. Indeed, a great virtue has been mentioned for one who dedicates herself to her orphaned children. However, if the father is unable to increase the financial support, and there is no way to combine custody with marriage, then she has no choice but to leave the children with him. But if it is possible to combine custody with marriage, for example, if the father does not demand the children and the husband agrees to them staying, then this is better and more appropriate.