Does the triple divorce take effect if I swore to my sister, "By triple divorce, you shall go down," because she refused to go to her parents' house, and then she got out of the car and went to her parents' house? Do I owe expiation? And does the triple divorce take effect?

The preponderant view is that what matters in oaths is the intention of the swearer. If there is no intention, then the reason for the oath is considered. Based on what is understood from the question, the reason for the oath was your desire for your sister to stay overnight at your home and not return to her father's house. Therefore, it appears that the oath has been broken by your sister's return. The fatwa issued by us is that breaking this oath results in the occurrence of triple divorce, leading to an irrevocable divorce (baynunah kubra), whether the intention was to effect divorce or merely to emphasize and threaten. However, some scholars, such as Ibn Taymiyyah, are of the view that the ruling on an oath by divorce that is not intended to effect divorce, but rather as a threat, is the same as an oath by Allah, and the swearer is obliged to pay an expiation for breaking an oath (kaffarat yamin), and no divorce occurs. When divorce is intended, one divorce (talāq wāḥidah) occurs, counted as three. Since the issue involves details and differences of opinion, it is advisable to present the matter to trustworthy scholars in your country. It should be noted that the lawful oath is to swear by Allah the Almighty, and swearing by divorce is among the oaths of the wicked and can lead to serious consequences.