All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If the reality is as you mentioned, your wife has committed a great evil by combining negligence of Allah’s right, and infringement of your right as her husband. She is obliged to preserve your rights and guard her chastity. Allah, the Almighty, said: {So righteous women are devoutly obedient, guarding in [the husband's] absence what Allah would have them guard.} [Quran 4:34] Commenting on this verse, Ibn Katheer said: “Al-Suddi and others said that it means she protects her honor and her husband's property when he is absent.”
Therefore, you should give her good advice and remind her of Allah. If she repents to Allah, keep her as a wife, treat her well, educate her on the principles of goodness and faith, link her to good gatherings, centers of memorizing the Qur’an, and so on, and be a role model for her in goodness so that she would be righteous and fearful of Allah and avoid places of temptation.
If she does not listen to your advice, consider the matter of parting with her by means of divorce or Khul’ and you should cover her faults and not tell any of her family of what she had done unless it is for a legal objective, in which case you should inform her guardian as much as needed to work on protecting and preventing her from seeking the means of corruption.
Allah knows best.