I've learned a lot from this site. And the main thing I have learned is that alcohol affects every aspect of a relationship. Even when the A hasn't drunk in a while and is seemingly sober, it still has an effect. Almost everything they say and do is focused on alcohol and when they will get to their next drink. Him throwing back your own faults and shortcomings is just quacking, him trying to get the focus off of him and his drinking. It's manipulation, something A's are very good at. I also have gleened that only you can truly decide your next steps in deciding what is right for you and your children. As a wise member here has said "I stayed until the pain of staying was greater than the pain of leaving" (I may have paraphrased a bit).
Keep coming back. SR is a tremendous source of support. Check out Al-Anon as well. I haven't gone yet (still working up my courage) but I intend to go soon. Support is key. Keep taking care of YOU and you KIDDO'S and let your H work out his issues on his own. They are his to own and his to resolve just like yours are your own.