For your "one-child policy", I guess you may be confused by that Asylee should file such petition within one year of arriving US, to that a child must be less than one year old.
For your "extreme hardship", I would like very much to know the result of your homework, although we may have different definition on term of "enough", specifically on how a parent can benefit from it based only on his/her USC child. With presumption that a parent of being unlawful presence may exclude himself/herself from removal proceedings by extreme hardship on the ground of his/her US-born child, it will be practical that anyone who comes to US to give a birth will stay lawfully in US.
I understood you were trying to offer help, and that is appreciated, while I did not think appropriate to offer unverified information, which might be misleading to a person who is currently at stake. So don't get it personal. It is your points got offended, not you.