Knowing that she was drunk makes me lean harder towards the abduction theory. If she was drunk and injured/killed the baby, then how did she cover it up so perfectly? I don't see how she could have kept it a secret form the older son or from the first people on the scene. I do not see how she could have disposed of the child so quickly. She would have needed help from an accomplice. So maybe she did it and had a friend/relative come over and clean up her mess. IDK It just seems pretty lucky that she had an accomplice available at such short notice to do such a hugely morbid favor for a drunk mom.
eta: I used to be a bartender. I know from experience that when someone is really drunk, they make a mess of anything they try hard to fix.