What is the ruling on the oath: "Do not ask my mother about my wife, and if she asks, I will divorce her," if the intention behind it was to threaten, not to divorce?

Your statement to your mother, "If you ask about my wife, I will divorce her," is merely a threat of divorce and not a suspension of divorce contingent upon her asking. So, if your mother asks about your wife, no divorce occurs, you are not obligated to offer expiation (kaffarah), nor are you required to fulfill this promise, nor is it even recommended, for "a promise of divorce does not take effect, no matter how many times it is uttered, and there is no obligation, nor is it recommended, to fulfill this promise."