Am I obligated to divorce my wife after discovering her relationship with another man and her going with him to a hotel, knowing that I made a vow to her not to divorce her, and she did not commit adultery with him, and I have two children with her?

If the wife repents from the forbidden relationship and no suspicion arises from her, then it is preferable to keep her and not divorce her, for repentance erases what came before it. However, if suspicion arises from her, then it is preferable to divorce her with expiation for the oath. It is not permissible to expose her to her family or others, because concealing a Muslim's faults is obligatory unless there is a clear benefit. The husband must fulfill his right of guardianship, close the doors to temptation, establish Allah's boundaries in his home, and cooperate with his wife in obedience, while having a good opinion of her.