Is a wife sinful who left her husband’s home and traveled with her child to her family without his consent due to deteriorating security conditions and to protect her and her child’s lives?

A woman must obey her husband in what is right. This includes not leaving the house except with his permission, based on the saying of the Prophet, peace and blessings be upon him: "If a woman prays her five [daily prayers], fasts her month [Ramadan], guards her chastity, and obeys her husband, it will be said to her: 'Enter Paradise from any of its gates you wish.'" This obedience is restricted to what is righteous. Therefore, obedience is not obligatory in matters that harm the woman or endanger her person, honor, property, or religion. Scholars have permitted a woman to leave her home without her husband's permission in cases of necessity, such as fear of the house collapsing, fire, drowning, harm from neighbors, or if the house is unfit for dwelling. This also applies if the husband is not knowledgeable and she faces a matter requiring a fatwa, or for performing the obligatory Hajj with a mahram. Accordingly, your sister is permitted to leave her home without her husband's permission in the case you mentioned, due to the intensity of the war, and there is no sin upon her. Her husband should fear Allah regarding those under his care.