Is it permissible for me to give my wife another chance after she confessed to her infidelity, knowing that I have committed similar mistakes? And how should I deal with the man she was involved with; should I file a lawsuit against him for adultery, or should I seek another way to get even with him without tarnishing the image of my daughter’s mother?

The remorseful and repentant wife should be given another chance, and there is a reward in that, for the Prophet, peace and blessings be upon him, said: "Whoever conceals a Muslim, Allah will conceal him." The questioner should repent and seek forgiveness, for what befell him might be due to his sin. They both should forget the past and open a new page. As for the other person, his matter is left to Allah. There is no benefit in filing a case against him due to insufficient evidence, and filing a case will lead to defamation and exposure of what was concealed. He should be patient and complain to Allah.