Is it permissible for a woman forced into an immoral act to commit it due to a credible threat of killing her child or husband, and the like?

Adultery is one of the major sins forbidden by Allah due to its consequences of lineage confusion and violation of honor. Islam has legislated the defense of honor, even unto death, and whoever is killed defending their family is a martyr.

If a person is coerced into committing a forbidden act, they should aim to avert the greater of two harms by committing the lesser. Valid coercion, according to the majority of scholars, is a threat to life, limbs, or similar severe harm. Mere insults or defamation are not considered valid coercion.

Scholars have differed on the validity of coercion if the threat or harm is directed at someone other than the coerced individual. Some Hanafis, Malikis, Shafi'is, and Hanbalis hold that coercion is valid if it targets parents, children, or unmarriageable kin (mahram). The Hanbalis even extended this to anyone whose torture would cause the person great distress, considering coercion against them valid.

Based on this, if a woman is coerced into adultery by compelling coercion (ikrah mulji'), and she cannot defend herself except by sacrificing herself for her child, husband, or anyone whose harm would cause her great distress, then it is permissible for her to do so. It is legislated for her and for them to defend themselves even unto death.