Did the man commit a sin by divorcing his wife after discovering she was a "bint haram," and how can he address the matter to avoid psychological harm to the children?

The fundamental principle in marriage is to prioritize religious commitment and character, with lineage being secondary. If a woman of noble lineage but lacking religious commitment is contrasted with a woman of humble lineage but devout, the religious woman is to be preferred, based on the Prophet's (peace be upon him) saying: "So win the one who is religious, and you will prosper." If a woman possesses good character, religious commitment, and noble lineage, then the one with lineage is preferred. As for this woman, if she possesses good character and religious commitment, then the man's marriage to her is correct. The fact that she is born out of wedlock does not harm, as it is a sin for which she is not accountable. Divorcing her for this reason would be burdening her with something not of her making. Therefore, the man must take her back.