What is the religious ruling concerning a man who discovered his wife's infidelity with his younger brother, knowing that they have three children and that the wife's family is known for its righteousness and commitment, and what should he do?

Accusing a Muslim of indecency without proof is a grave sin, especially a husband accusing his wife. Furthermore, entertaining suspicions leads to spying, which is forbidden by Islamic law. There is nothing in the question's premise that proves the occurrence of adultery; therefore, one must repent from this false accusation. If there is a cause for doubt, then jealousy is commendable, and the husband must safeguard his wife by guiding her towards modesty and religious upbringing, and by being a good role model. He must also adhere to Islamic guidelines regarding the entry of non-mahram individuals, especially the husband's relatives.