At the time of birth, if a choice has to be made between the mother's life or the child, what should one do?

Answer

The choice of the mother or child living is satanic. Murder of the child may not be committed on the basis of the satanic notion that the child's murder will save the mother's life. It is absolutely haraam to make such an evil satanic choice. Under no circumstances is such satanic villainy and infanticide ever permissible. Whoever is destined to die, will die at the appointed time with the permission of Allah Ta'ala. The type of fear mentioned in the question stems from an attitude of kufr.