Does divorce occur by saying, "If you meet this person, I will divorce you," with the intention of threatening, and is it permissible to retract this statement and allow my wife to see this person, and what is the expiation if the wife does so without my permission?

Your statement to your wife, "If you meet this person, I will divorce you," is a promise of divorce. Nothing comes of it unless you actually divorce her.

Therefore, you may permit her to see this person if seeing him is permissible. And if she sees him without your permission, no divorce takes place and no expiation is due, because it is merely a promise of divorce and not an oath or a conditional divorce.