What is the ruling on a young wife, whose husband has passed away, observing her 'iddah in her family's home, whether she has an independent home or was living with her husband's family, and she is caring for young, underage children?

The place for the 'iddah (waiting period) of a divorced woman or a widow is the marital home she inhabited before the separation. This is the view of the majority of scholars. The evidence for this is Allah's Almighty saying: "Do not expel them from their houses, nor should they themselves leave" (Quran 65:1). The verse attributes the house to the woman, and it is her house where she used to reside. 'Umar, 'Uthman, Ibn 'Umar, Ibn Mas'ud, Umm Salamah, and others mandated observing the 'iddah in the marital home. However, it is permissible for a woman to observe the 'iddah elsewhere if there is a valid excuse, such as fear for herself or for the house.