A woman confessed to her husband that she committed the heinous sin of adultery. What should he do, should he remain with her or divorce her?

Shaykh Muḥammad Nāṣir al-Dīn al-Albānī:

If he is pleased with her in terms of her religion and she has only slipped due to the influence of Satan but has now repented and turned back to Allāh , then he can keep her or he can divorce her. 

However, what is most likely to be the right course of action depends on the particular circumstances of the wife. If she is a righteous, praying, fasting woman who slipped up and committed adultery, it is permissible for him to keep her if she confessed and repented to Allāh . But if she is always looking for ways to disobey Allāh , then there is reason to fear her. Is that clear?