... This is a test of theoretical systems of morality, not what someone would literally be able to do.
Of course, and I didn't mean to speak for everyone and sort of scoff with that statement.
As for WHY I believe it to be ethically impermissible, taking the baby's life involves imposing on its right to live and in most cases, putting the mother and likely the person who killed the baby through emotional trauma afterward. For those that say it is better than the alternative (death), know I staunchly disagree.
Now, what about the others' right to live? They too have a right to live, and in order to defend that right they'll have to be aggressive in their attempts to usurp control of the baby and then kill it. I'd like to believe that in all hypothetical cases, the mother would probably not be okay with the idea of her baby being killed at the expense of the them likely living. Who is to say that after the baby is killed that the mother won't break down and start sobbing? This would be an equally difficult problem to surmount.
With arguments about utilitarianism rising, I think it is time to speak upon my preferred system of utilitarianism, which is preference utilitarianism. I think the decision whether or not to kill the baby really lies in how many people actually want to kill it as opposed to those that don't, and how adamant the mother is in not letting anyone kill it. If the mother truly doesn't want it to be killed, then the baby should not be killed; regardless of what others want. The value of human lives and the value that others feel FOR a human life cannot be measured, so it is not as if killing one person at the cost of the mother is justified even if everyone else wants to kill it.
Although I know this is a hypothetical scenario, it is presented in a way that is logically fallacious (false dilemma): in reality, there are a number of things that could be done to quiet the baby aside from killing it.
Ethically speaking, I still strictly conform to the view that you should not kill the baby. However, I do not have any personal qualms with it being killed.