Does saying "You are divorced by three" twice constitute a divorce, knowing that this is the first time this has happened and both parties are regretful and reconciled on the same day?

The word "divorced" is among the explicit terms for divorce. The fact that it was uttered while angry does not prevent its occurrence, unless the anger was so severe that one did not know what he was saying. Your statement to your wife: "You are divorced with three" is an explicit term by which a triple divorce occurs according to the majority of scholars, and this is the fatwa we adhere to, contrary to Ibn Taymiyyah. Therefore, according to the fatwa we adhere to, if you uttered the divorce consciously and not overwhelmed by your intellect, then your wife has become irrevocably divorced from you with a major separation (baynunah kubra), and there is no way for you to return to her until she marries another husband willingly, and he consummates the marriage with her, then divorces her or dies, and her waiting period from him expires.