What is the ruling of the religion on a mother who committed adultery and gave birth to a child out of wedlock before the death of her husband, and without waiting for the iddah, then married her lover, and what is the status of this child born out of wedlock in relation to her legitimate children after the cessation of their relationship for ten years?

If what was mentioned about the woman is true, then she has committed three major sins: adultery while being married (her punishment is stoning), betraying her husband and bringing a child not from him into his bed, and violating the sanctity of the iddah (waiting period) and her husband after his death. Pleasing the mother should be in matters that do not involve disobedience to Allah, and it is an act of righteousness towards her. It is not permissible to sever ties with her or abandon her. As for the daughter she bore, she is attributed to her father (the mother's husband), based on the Prophet's (peace be upon him) saying: "The child is for the bed, and for the adulterer is the stone." She should maintain ties with her just like her other sisters.