Aw hugs Jess, that is such crappy timing. Is it possible that he is feeling this way because he is scared? Is there any chance that after the Lyla has arrived & you guys a re settled that you may be able to sek some counselling & patch things up?
Can he move out? You shouldn't have to be the one that has to leave given your current state. Also with a new baby what does he want you to do? Thats a bit rough.
maybe contact your hospital & ask to speak with the social worker there. They should be able help & support you.