I applaud you for writing this and you did put it in context in another post (no kids, never lived together). Buffalo66's example stood out for me in that he reflected the pain she felt and not just apologized for his behavior.
It is a good letter overall. Maybe if you probe a bit deeper into how some of your actions made her feel it would express how sorry you are. Addressing someone else's feelings are tricky but acknowledging that you know your actions caused great pain is an awesome step in recovery.
best of luck