Does divorce occur if you swore to your wife that she would be divorced if she left the house, then your mother opened the door for her, saying, "Go out, may God make it easy for you, my daughter"?

The fatwa (religious edict) is that swearing by divorce causes divorce to occur upon breaking the oath, whether the swearer intended to cause it or not, unless the wife left under duress, and her fear of being beaten is not necessarily duress. If a divorce occurs and it is not the third one, you can take her back before her waiting period (iddah) expires. However, according to the opinion of Ibn Taymiyyah, if you intended to threaten and did not intend to cause divorce, then divorce does not occur, and you must pay an expiation for an oath. Swearing by divorce is among the oaths of the dissolute.