Does divorce occur, or am I bound by an oath of expiation, if I said to my wife in a moment of anger: "By divorce, I will not go with you to buy something," when my intention was that her sister should not go to buy something for herself? What is the ruling?

This phrasing is considered an oath. The majority of scholars hold that divorce occurs when one swears by divorce and then breaks the oath, and this is the most preponderant opinion. If you swore by divorce to go shopping with your wife and her sister, then divorce occurs if you go with them in the manner you intended, but you do not break your oath if you go with them in a manner other than what you intended. An oath is specified and restricted by the intention of the swearer; if he intends by his oath something that it can bear, his oath is directed to that. The occurrence of divorce here, if the oath is broken, is what the four madhhabs agree upon and it is the most preponderant opinion. Sheikh al-Islam Ibn Taymiyyah said: You are obligated to perform an expiation for an oath (kaffarat yamin) if you did not intend divorce. In the event that divorce occurs, you may take your wife back before her 'iddah (waiting period) is complete, provided this divorce does not complete the three (divorces). Anger does not prevent the occurrence of divorce unless it reaches a state where the person does not comprehend what he is saying.