What should I do now that I have discovered my wife's relationship with another man, despite my certainty of her sincere repentance and deep regret? Should I divorce her, or should I keep her with her children and abandon her, or should I forgive her for this sin and pray for my heart's healing? And if I do that, would I be a cuckold?

The questioner is congratulated for repenting from the sins and transgressions committed, for Allah loves repentance and rejoices in it, and replaces bad deeds with good deeds for whoever repents with a sincere repentance that fulfills its conditions: abstaining from the sin, regretting having committed it, and resolving not to return to it.

As for the wife, if her repentance is sincere, and she regrets what she did, and her condition has improved, and her disobedience has not negatively affected the husband, then it is better to keep her to preserve her repentance and the children, especially since the husband was negligent towards her before her repentance. The husband must help her achieve sincere repentance and guide her towards good, and prevent her from associating with those who might corrupt her. It is preferable to conceal her past and remain with her after her repentance, for keeping her after repentance is not a sign of lack of jealousy. And Allah knows best.