What should a man do who discovered that his wife is talking to another person via Facebook, both by voice and writing, and he has conversations proving this, and she admits the mistake but threatens to expose certain sexual practices if he does not lie about the ownership of her Facebook account to his family, knowing that they have two children, and she is a stubborn person who shows no interest in divorce?

If the narration of the wife speaking to a non-mahram man is authentic, then she is disobedient and negligent in her husband's rights, and divorcing her is recommended. However, do not hasten; instead, advise her and call her to repentance. If she repents, then keep her; otherwise, separate from her. You erred by informing your family, as concealing the sinner is required. Anal intercourse with a woman is forbidden, and repentance is obligatory upon both of you. The husband should satisfy his wife's emotional needs, and the wife must obey her husband and not leave without his permission. The wife's maintenance is estimated by sufficiency, and you should be generous to her without extravagance.