Is it permissible for a wife to separate from her husband internally (i.e., live without cohabitation) after he marries another woman, given her feeling of psychological harm and her desire not to divorce for the sake of the children, and is she considered wronged in this situation?

A woman who discovers her husband has married another experiences deep disappointment and a sense of injustice, but she must overcome these feelings and consider the assets she possesses, such as her loving husband and children, and not jeopardize them with hasty decisions. Islamic law does not permit a woman to seek the divorce of her "sister" in order to monopolize her husband, for the other wife is her "sister." This marriage is not considered an injustice according to Islamic law unless the husband falls short in upholding justice. This is a trial that requires patience and contentment, and one should not destroy the household because of it or because of natural jealousy. Both women and men naturally need each other, so a woman should not defy her innate nature by internal separation, and the husband has a right to intimacy with his wife. If the wife refuses to fulfill this right, the matter rests with her husband: if he foregoes his right, that is his prerogative; but if he refuses, she has no right to remain married to him in this state.