What is the ruling of Islamic law regarding a wife who exchanged messages and pictures with her former colleague and went out with him without her husband's knowledge, then repented? And should the husband divorce her given the presence of children?

If the wife has repented and committed to wearing the hijab, then the past should be forgotten, and the future looked forward to, for "the one who repents from sin is like one who has no sin." Spying is blameworthy in Islamic law unless there is a strong suspicion. Do not divorce your wife if she has become righteous; divorce is disliked without a valid reason.

One should be diligent in nurturing the wife's faith, placing her in a safe environment when traveling, and striving for residency to protect yourself and your wife from temptations.