Is it permissible for a divorced mother, who is ill, to take from the maintenance of her two daughters for medical treatment, knowing that their father provides for their food and drink, and that she is compelled to do so?

The fundamental principle is that a mother who is a custodian (حضينة) should not take from her children's maintenance allowance for her custody; rather, she is entrusted with the money to spend it for their best interests.

However, it is permissible for both the father and the mother to take from their children's money to meet their needs, provided it does not harm them, because "A man's child is from his earning, from his purest earning, so eat from their wealth." The mother may take from her child's money to meet her needs, as long as it does not cause harm to the child.

Based on this, it is permissible for you to take from your children's money for medical treatment, provided that it does not harm them, meaning after their needs have been sufficiently met.