Does divorce take effect or is an expiation for breaking an oath (kaffarat yameen) incumbent upon one who swore to his wife by divorce that she would not leave the house on a specific day, but she left after several days?

If you conditioned your wife's divorce on her returning home after leaving it, and she did not leave in the first place, then the divorce does not occur due to the absence of a breach of the oath. And if, by your oath, you intended her return only on a specific day, then her leaving on another day does not affect it, for intention has an effect on the oath. One should be wary of stirring up problems and avoid uttering words of divorce.