There have been a lot of replies to your question and they have all been pretty much correct. Basically, as stated, the baby would become a U.S. citizen and can either remain in the U.S. or return home with you. Your leaving the U.S. as scheduled is important as you could soon become considered an Illegal Immigrant (alien) in the U.S. of you fail to leave as required by law.
The U.S. is facing major problems due in part to the Constitutional amendment that allows for U.S. citizenship status as you suggest. Many immigrants come here, have their babies who automatically become U.S. citizens, then the parents refuse to leave thinking they too can later become U.S. citizens. When the parents are arrested for being here illegally they are deported and they then claim the problems were created by the American people; Americans are getting fed up with the illegals committing the crime and then refusing to take responsibility for it.
Based on that there is building pressure to make changes in the U.S. constitution that will do away with the provisions allowing the babies to automatically become U.S. citizens. The amendment is old and although it was applicable when passed in 1868 it no longer has pertinence or is appropriate for modern society. Doing as you suggest will most likely create problems for you AND the child in the future as the American people are fed up with the problems being created by the illegals here that are collectively costing the U.S. close to 900 Billion dollars a year.
I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.