Hi Least,
You show a great amount of integrity and honesty by posting here and accepting the work that must be done on yourself and your relationships. I never got an apology from either of my alcoholic parents, and my mother never pursued recovery (pretty much stopped at Step 1 - powerless). I attend an AA meeting in part to see the recovery in others that I never saw in my parents. So, I am really impressed by one like yourself who is diving right back into parenthood, warts and all.
As much as it is necessary to make amends, please stay focused on your own recovery. I think your kids will appreciate the hard work you are doing on yourself, and it is a good model for the work they have to do on themselves. Yet, expect some disappointment, anger and bumps in the road from them - patience is and will be a necessity.
You might also consider talking to counselors experienced in alcholism in families. It may be helpful to look into family counseling. And Alanon/alateen are very helpful groups. There may also be ACOA-specific meetings in your area. And keep posting whenever you need feedback!