Killing someone by a reckless and illegal act probably falls short of murder. Manslaughter? It is difficult to separate emotions from the law in this sad circumstance.
Yes, you are correct.
I find it so repulsive, though, that a mother blessed with a beautiful little child could be so vile as to do such a thing. I don’t understand how you don’t have your child’s interests, not your own, at heart. I just don’t get it.