If I had saved my Mother*, she would have murdered me for not saving the baby.
-* She died about 4 years back.
My mother. Imagine if this same situation happened when that schmuck Hitler was born, or Mao, or Stalin?
Unless you created the situation that put either in harm's way, you have nothing to do with the loss of life. You are saving someone's life because you were able to and in many cases, putting yourself in a life-threatening situation to do so. That act is noble regardless of other events happening nearby. At that same moment thousands of people are dying across the globe, the one in close proximity is as much your fault as everyone else's, which is none.
My answer is that I'd save the baby, and then I'd do what I could to save my mother.
Depends on some important issues. In some cases it would be my mother, in others it would be the baby.