Point of view
The Founders believed that the indivual's right to arms was a natural right (or a God given right, if you prefer), and wrote the 2nd Amendment as a curb on Govt abuse of the natural right. It does not grant us a right to arms, simply being here on this earth and drawing breath grants us our right to arms.
Govt. can, through force, forbid you the exercise of your right to arms, but cannot remove it, as Govt does not grant it.
As to the birth right of children of the undocumented, they have the same natural rights as all men. Citizenship status is a political decision and has nothing to do with natural rights. It may be granted or denied at the whim of the Govt.
To play your game, I would without hesitation choose the 14th Amendment, as I don't give a rat's *ss about the "rights" of children of the undocumented.