My wife is having love stories on the Internet

All praise be to Allah and peace be upon His Messenger, upon his family, his Companions, and those who follow him.

Dear valued brother, the negligence of man, at all levels, to his wife does not push a righteous woman to cheating or looking for the missed passion, but only women who have the nature of cheating do that. People hardly know the truth from falsehood, and guidance from error, but chastity is crystal-clear and does not need a proof or an explanation; people only do not have the desire to follow the truth or choose the correct way.

Dear brother, you did not tell us about her reaction, did she regret and repent or not? You are asked to examine her way of talking and her speech. If you think that she is telling the truth and she ended her relationship with that person and regretted her action, forgive her and treat her as a repentant because the Prophet of Allah (peace be upon him) said: "The one who repents of his sins is like those who have no sin." [Reported by Ibn Majah]

Moreover, cut the Internet, take her mobile, and put her under surveillance for a while to be sure of her truthfulness, and when you are sure of her truthfulness, live with her normally and try to fix her behavior.

However, if you become sure that she is untruthful or likely doubted her truthfulness, or the signs of regret, repentance, and integrity did not show up on her, divorce her. Do not be afraid for your children, for Allah shall undertake them with His Protection and care as long as you are righteous and away from sins and faults. "But if they separate (by divorce), Allâh will provide abundance for everyone of them from His Bounty. And Allâh is Ever All-Sufficient for His creatures' need, All-Wise." [Surat An-Nisa': 130]. Marriage is based on intimacy, mercy, or on obligations and preserving rights, but if the wife does not pay attention to these matters and yearned for another man other than her husband without regretting or repenting sincerely, she is not righteous. We cannot tell the husband to live in a prison of doubts, dishonesty, and real schizophrenia. However, if you prefer the first solution, cover on her because the one who covers a Muslim in the world, Allah shall cover him on the Day of Recompense.

May Allah guide you to goodness!