What is the ruling in Islam regarding a mother's custody of her young children after the death of their father, given that she is divorced?

The ruling of Islam concerning the custody of children before the age of discernment, when parents separate, is that the mother has a greater right to it and is more deserving due to her complete compassion, care, and the child's need for it. This is based on what was narrated in Sunan Abu Dawud, that a woman said: "O Messenger of Allah, this son of mine, my womb was a vessel for him, my breast gave him drink, and my lap was a refuge for him. And his father divorced me and wants to take him from me." So, the Messenger of Allah (peace be upon him) said to her: "You have a greater right to him as long as you do not marry." Her entitlement to custody does not depend on his life or death; rather, she has this right after separation, unless she is characterized by an impediment such as immorality (fisq) or the like.