You became self aware and that helped with your development and understanding your own behaviour. That is so admirable because it is not always easy. Your example with your father and all the pacing - shows how important apologising to him meant for you.
With your friend, it is very humbling and heartfelt when you put ego aside and made that effort to apologise. It is understandable that you were relieved and I am certain your friend was as well. Thereafter, your friendship can go to another level based on the sincerity uttered with those magical words.