Does my oath to hit my sister with a shoe, made in a moment of anger if she does something I dislike, count as a laghw (vain) oath, and do I owe expiation for it?

This oath is not a vain oath (laghw); rather, it is a binding oath (mun'aqid) that necessitates expiation (kaffara), which is feeding ten poor persons or clothing them or emancipating a slave. If you are unable to do that, then it is fasting for three consecutive days. You must break this oath, because it is an oath to commit a prohibited act, which is striking the face with shoes.