Just to clarify, again, I am not saying the mother was not horribly negligent in her actions. And you are correct, if not for her actions (or the in-action of her husband) the baby would, most probably, be alive today.
Given your personal experiences with alcoholics (which you have alluded to on this thread), it is understandable that this particular situation would hit very close to home for you.
For reference purposes, one definition of murder (there are probably many, I'm sure) is:
mur·der
   [mur-der] Show IPA
noun
1.
Law . the killing of another human being under conditions specifically covered in law. In the U.S., special statutory definitions include murder committed with malice aforethought, characterized by deliberation or premeditation or occurring during the commission of another serious crime, as robbery or arson (first-degree murder), and murder by intent but without deliberation or premeditation (second-degree murder).
http://dictionary.reference.com/browse/murder
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Based upon this definition, I don't find that the mother had a)malice aforethought; b)did not premeditate; and had no c)intent to kill her child.
She killed her child through her actions. But was it murder, or negligence due to her drinking? And would that make her husband an accessory, because he did nothing to stop it?