What should I do with my wife who confessed to committing adultery with my brother during my absence, even though she claims to have repented sincerely? Should I divorce her, or should I continue to live with her and conceal her sin?

No tribulation befalls a servant except due to his transgression of the Prophet's commands, among which is the command not to seclude oneself with women, especially the relatives of the husband. The Prophet warned against entering upon women and likened the hamw (male in-law) to death. Al-Nawawi explained that the hamw refers to the husband's male relative whom she would be permitted to marry if she were not already married. If the wife has repented with sincere repentance, then conceal her faults and keep her, while being cautious not to allow any non-mahram (definition) man to enter upon her in the future. However, if it is highly probable that she has not repented, then divorce her kindly, conceal her faults, keep her secret, and use equivocation if asked about the reason for the divorce, while being aware of the danger of prolonged absence from the wife.