His behavior is not simply because he is an alcoholic, it is because he is an abuser. Look at how well he could keep on his "mask" of nice while others were around.
If you're a bad mom for making a mistake, then what about all his intentional abuse in front his boys?? Seriously, IMO, your STBXAH has to be the most abusive men I have read about on SR. Be thankful, you have made the break.