1- The hadith from the Imam about the Siwak basically means you cannot hurt your wife. If she is insisting on her wrong and you must discipline her, then do it in a way that she does not get hurt. The point is to let her know her behavior is not welcome.
2- As for the hadith about not hitting one’s wife, this is the general instruction. It’s haram for a believer to hit his wife. Some men think it’s completely ok. It is not. Yes, there is an exception which the verse refers to. However, when the conditions of the exception are fulfilled, one must make sure not to hurt her or leave any marks. It must be gentle.