What is obligatory upon one who learns that his wife is committing fornication?

This is a message from the questioner (A. S.), a Syrian national residing in Riyadh. He says in his message: I am married, and five years after my marriage, I learned from one of the neighbors that my wife is committing fornication. So I observed it and found it to be true. What I did was hit her. She asked me for divorce more than once, but I did not divorce her out of fear that the children would be scattered. If I divorced her, I have no money to remarry. I am an ordinary worker; some days I work, and most days I am without work. Please advise me on what I should do. May Allah reward you.
Answer: This is one of the great calamities, and it is obligatory to treat it through discipline and advice, by reprimanding her and making it clear to her that it is obligatory for her to maintain chastity and to be cautious of what Allah has forbidden for her. Indeed, fornication is among the ugliest crimes and the greatest of major sins. Allah has threatened the fornicator with severe punishment. He, Exalted and Majestic, said: We seek refuge in Allah... He threatened the fornicator that his punishment will be doubled for him, and that he will remain in it in a state of humiliation on the Day of Resurrection in the Fire. We ask Allah for safety.
And the Prophet (peace and blessings be upon him) said: This is a sign of weak faith, or the absence of faith. We seek refuge in Allah. So the husband should observe her, take care of her, and discipline her if she does any of this, or if he finds signs of any of it. He must discipline her with deterrent discipline, along with preaching and reminding her of Allah, and that this is an abomination and a sin against Allah , and one of the causes of separation. If she reforms, praise be to Allah. If she does not reform, he should separate from her and divorce her, so that she does not bear him children from another man. Whenever she reforms, repents, and returns to Allah , praise be to Allah. The door of repentance is open, and whoever repents, Allah accepts his repentance if he is sincere. However, if she does not return and repent, and continues in her bad state, then such a woman should not remain, rather she should be separated from and not kept; because this brings much evil upon him, in himself, in his children, and in his reputation. There is no power and no strength except with Allah! Yes.
The presenter: Do you not direct the Shaykh’s Grace to closing the doors that lead to such things, such as the laxity in the mixing of women and men, and the entry of non-mahrams?
The Shaykh: Yes, that is also correct. It means he should take care to close the doors that lead to this thing, such as preventing her from going out, and such as not allowing her to mix with wicked women, whether neighbors or others, if this is feasible for him. This is one of the most important matters: that she does not mix with the bad ones, that she does not go to the markets, and that she strives to observe the hijab. But if one is accustomed to fornication, and may Allah protect us, she will obtain it even by telephone, we ask Allah for safety, and she is in her house, we ask Allah... But in any case, one should take the means as much as possible. If it is her habit to go out, he prevents her from going out except out of necessity. If someone bad enters upon her, he prevents the bad person from entering. If she goes out to neighbors who are not good, he prevents her from doing so, and so on. That is, he takes the means...
The presenter: And going out to non-mahrams, meeting non-mahrams, many people are lax in this?
The Shaykh: Yes, her going out to non-mahrams, to her uncles who do not have faith, or to others, all of this means: he must strive to prevent the causes of evil as much as possible.
The presenter: May Allah reward you with good, and may Allah bless you.