What is the legal ruling regarding a man's statement to his wife: "You are divorced from me if you do this today, unless I am pleased with you and desire that," and then he becomes pleased with her after a day? Does this necessitate an expiation for an oath or is it considered a divorce?

If you swore an oath of divorce upon your wife that she would not do a specific thing except with your consent, and she either did not do it at all or did it with your consent, then there is no consequence for you. However, if she did it without your consent on the intended day, the divorce becomes effective and enforceable according to the majority of scholars, and this is the preponderant opinion. You may reconcile with her if it is not the third divorce.

Ibn Taymiyyah chose the expiation for breaking an oath (kaffarat yamin (definition)) if you did not intend divorce. After the specified day ends, the conditional divorce is dissolved, so nothing is binding upon you if your wife does the action on another day. One must be cautious about swearing oaths of divorce.