Does a divorce that was not intended to take place, but rather was uttered to calm things down, actually occur?

What you uttered is considered a lie and does not affect 'isma (infallibility/inviolability), because it falls under the category of reporting, not enacting. As long as you did not intend to make your wife's divorce conditional through an enacting statement, but rather wished to appease your mother with something that did not happen, then what you uttered is not considered a valid condition. Rather, it is a lie that should not be indulged in or trivialized, as there are other ways to appease one's mother and solve problems without resorting to falsehood. Lying is not permissible to resort to unless it becomes the only way out.