What is the effect of the father-daughter relationship, declared by the husband with his daughter born of adultery, on his daughters from his wife, especially with the wife's fear of the matter being exposed and its impact on her religion, mental health, and the upbringing of her daughters?

If what is mentioned in the question is proven, then the girl's lineage would be attributed to her father if she was conceived while her mother was still married to her mother's husband, based on the Prophet's (peace be upon him) saying: "The child belongs to the bed." If she was conceived after her mother divorced her husband, then her lineage would be attributed to her mother; she would be a child of fornication and not your husband's daughter.

The girl is considered your husband's stepdaughter, and she is one of his mahrams if he married her mother and consummated the marriage with her.

It is necessary to discuss this matter gently with the husband and emphasize the importance of determining the girl's lineage, because his claim of fathering this girl might have a negative impact on your children and on the girl herself if people discover that she is a child of fornication.

It is not permissible for the wife to return to her family or leave her husband's house without his permission.

If the husband is a liar, deceitful, and breaks covenants, he should be advised kindly and prayed for guidance. If the wife is harmed by staying with him, she has the right to seek divorce, keeping in mind that divorce is not always the best solution, especially when there are children involved.