Congratulations, Chung, on your two weeks of sobriety. Good for you!!
In my experience, the people who have hurt me but that I have found the easiest to forgive are the ones who have "owned it," who have allowed me to express my thoughts and share my feelings about what they did and didn't try to shut me down ("I SAID I was sorry! Do we have to talk about this right now?" or make me feel sorry for them in some way or short-cut the process. Actually listening to your daughter, apologizing (every time), being sober and present and "walking your talk," as they say, will go a long way towards healing. As she sees you not only not drinking but digging deep to be the healthiest (mentally, spiritually, emotionally) woman you can be, your actions will speak louder than any words about how sorry you are for what you said and did while drinking. It's gonna take a lot of time, but each time she sees you say "No, thanks" to a drink, she's going to know she's more important to you than booze is. I wish you all the best.