Is a woman's marriage with the intention of khulʿ considered invalid if her ex-husband takes her children from her, or if her new husband abuses them? And what should she do if doctors refuse to allow her to fast?

A wife's intention to separate from her husband through khul' (divorce at the wife's instance) due to the husband's mistreatment or the loss of her right to child custody does not affect the validity of the contract. The intention that matters is the husband's, because he possesses the right of 'ismah (power to divorce). There is no sin upon her in this marriage. If the khul' takes place, her right to child custody will be restored to her. However, if marriage is not available for the woman, she must be patient and practice chastity.