A better life as a political tool?
Yes.
It would appear that the parent took a calculated risk...and felt that sneaking into America would provide better opportunities for her kid than living in Mexico. I think she's correct. To her, that was worth risking deportation. My grandparents considered the same thing. If I was in her shoes, I think I'd sneak her too.
You guys can debate the matter of birthright citizenship and whatnot, I think thats another matter...but having the kid move BACK to Mexico sort of defeats the whole purpose right?