Should the brother's wife be informed of his marriage to another woman, knowing that he married her out of his desire to have a child and because he engaged in unlawful sexual acts with her that his wife rejects?

The objectives of Islamic Sharia include protecting honor, so it is not permissible to accuse a Muslim of immoral acts based on mere suspicion. Such accusations may necessitate the Hadd punishment for slander. If it is proven that your brother committed immoral acts such as fornication (zina) or anal intercourse with his wife, he must repent. Fornication with a married woman is even more heinous. As for marriage without informing the first wife, her permission is not required, and we advise against informing her to avoid exacerbating problems. A child born to a married woman is attributed to her husband, and it is not permissible to attribute him to anyone else.