Is a divorce effective if you swore by it not to eat at your mother-in-law's house, and then you ate?

Your divorce occurred due to your breach of the oath. If this divorce does not complete the three divorces, then you may reconcile with your wife during her 'iddah (definition) (waiting period). Some scholars, such as Sheikh Al-Islam Ibn Taymiyyah, hold the view that divorce does not occur if you swear by it without intending to effectuate it, but rather with the intention of emphasizing something, and in this case, an expiation for a broken oath (kaffarat yameen) is required of you. It is advisable to avoid swearing by divorce, as it is considered an oath of the wicked.