I agree with the other posters who recommend Al-anon. It will help so much -- no one will tell you what to do but they will share how they handled similar situations.
You can also bring your kids to Alateen.
The guilt, relief, sadness, anger and anxiety that you and the kids feel is quite normal. After living with an active alcoholic, our own thinking becomes distorted. We DO wonder if we are to blame, if we could have done more, etc. etc. That is part of OUR Al-anon disease and attending meetings really helps us learn to put our feelings and behavior into perspective.
Another thing that really helped me: there are people in Al-anon brave enough to share that they love an alcoholic. I felt so sad when I read your location "ashamed ville." I completely understand. I felt so stupid for loving an alcoholic. I've hated a lot of alcoholics over the years. But when I fell in love with one as an adult, I was absolutely mortified. I couldn't believe I had made such a mistake.
But it was not a mistake. It was what it was. I love an alcoholic. He happens to not be part of my life anymore -- which is a huge relief. But I love him and that's okay. Accepting that is actually part of what made it possible for me to let him go completely.
I wish you the best and good luck at your meetings.