Does a divorce take effect, or is it an oath, if the wife goes to complete the procedures for her leave after you gave her the choice between you and her work, and you made her divorce contingent on her going to work, then you both agreed that she would complete her leave and submit her resignation after a year?

If you made your wife's divorce conditional on your mother going to work, with the intention of threatening her, then the oath is broken when your mother goes (to work) in the manner you intended with your oath. What matters in oaths is the intention. So, if your intention was to prevent your mother from returning to work on a permanent basis, and not to prevent her from going at all, then you do not break your oath if she goes to finalize vacation procedures.

However, if by your statement: "And by divorce, if she goes again, that's it," you intended that you swore by divorce that if she goes to work, you will boycott her, then your oath is not broken merely by her going, but by her going and you not boycotting her. If the oath is broken, the fatwa (definition) (legal opinion) we adopt is that the divorce occurs. Some scholars, however, are of the view that it does not occur, and a kaffarah (definition) (expiation) for an oath is sufficient.

Know that the right of a mother is great, and it is obligatory to treat her kindly and not to harm or threaten her. Swearing by divorce is among the oaths of the dissolute, and one must beware of it.