I do agree with your sentiment that if you only apologize for things you did then that makes it more sincere. However, it was taught to me that amends werent merely apologies but a willingness to make the person you harmed whole again. For me that is a much deeper action than an apology. I think that is where the idea of ' living amends' comes from.
As an example I am a recovering alcoholic and codependent like you and I am also married and a mom. So, for me I didnt just say I am sorry for making life hell. I told them each individually and when we were alone that I was sorry for causing so much pain, chaos, and uncertainity in their lives because they not only couldnt depend on me they didnt know how nuts I would be on any given day. I said it was my intention to earnn back their trust and be the parent/spouse they needed. I also told them I would always listen to them if they wanted to talk about things no matter how bad or uncomfortable it made me. And I still apologize for things as I remember them and I havent had a drink in 37 months