Does ẓihār apply to the wife by saying: "If you do such and such, you are unlawful to me unless I ask you to do that," and what is the expiation required in this case?

If you uttered the oath while overcome in your mind, it is a baseless oath (laghw) and carries no legal consequence.

However, if you uttered it while conscious, then the oath is binding, and its ruling is the same as an oath by Allah, as long as you do not know your intention at the time of swearing.

It is stated in Tuhfat al-Fuqaha': "If a man says to his wife: 'You are unlawful to me,' or 'I have made you unlawful to myself,' or 'You are unlawful to me,' he refers to his intention. If he intended divorce by it, then it is an irrevocable divorce as we have mentioned. But if he intended prohibition and did not intend divorce, or had no intention, then it is an oath."

Therefore, if your wife violates your oath, not out of forgetfulness of your oath nor misinterpretation, then you must offer expiation for an oath: feeding ten needy persons, or clothing them. If you cannot find them, then fasting for three days.