What is the ruling of Islamic law regarding a case of adultery between a married man and a married woman who refuse to repent, while avoiding scandal and the ruin of households, and is it permissible to inform the woman's family?

You must denounce the abomination to its perpetrator, warn him of Allah's punishment, and urge him to repent. If he does not repent, then threaten to inform those who can deter him from the evil. If he stops, then praise be to Allah. But if he persists, inform whoever is capable of restraining him.