Is it permissible for a husband to keep his wife after discovering her infidelity, with evidence available and her desire for divorce, for the purpose of protecting the children from dispersal and avoiding scandals that might affect his married daughters, and is the husband considered a "dayyūth" in this case?

It is not permissible to practice magic on one's wife, even if the intention is to reform her, because it is one of the gravest sins and destructive acts. The Prophet, peace and blessings be upon him, said: "Whoever comes to a diviner or a soothsayer and believes what he says has disbelieved in what was revealed to Muhammad, peace and blessings be upon him."

As for dealing with a disobedient wife (nashiz), begin by advising her and reminding her of God. If she does not obey, then abandon her in bed. If she still does not obey, then strike her with a non-violent beating. If she does not desist, then let recourse be made to judicious and knowledgeable people from the family without explicitly mentioning the matter. You are not a cuckold as long as you have zeal for your honor.