Piano, stop worrying about him and focus on you and baby - the most impt people there are. He is the one missing out - you are the lucky one to have brought your lovely baby into the world.
Try to leave off emailing him and pointing out his inconsistencies - you are merely reinforcing his huge sense of inadequacy. It is easier for him to blame you for what goes wrong than to blame himself. Blaming himself would mean taking responsibility which he doesn't want to do. Denial is a powerful aid to avoiding yourself. My WH is a master at it. It's like he is Jekyll and Hyde - is able to totally deny things that he did or said even if they were yesterday. A counsellor once told me this is a self-protective mechanism - facing up to the truth of what my H has done would probably make him go into such a depression he would not find his way out. I believe this to be quite likely and have seen this happen for brief periods when he opens his eyes - he quickly shuts them again though as he doesn;t like what he sees.
So leave your H to his own issues and just look after you and baby!
Me: 39, H: 37 Married 12 yrs EA 01/07, bomb 07/07. He moved out 09/07. Lived alone for some time, moved in with OW in 2009, moved out again Mar 2010 S:8 D:11