[DoodleDawg]

I say NO. The illegal mothers are not subject to the jurisdiction of the US.

Yeah they are. If they break the law then they can be arrested, tried, convicted, and jailed. That sure sounds like 'subject to the jurisdiction' to me.

[Red Steel]

They are subject to the local laws like traffic laws, but "Subject to the jurisdiction thereof" is a real reference to their country of citizenship.

The word "thereof" meaning from that cause or origin of foreign country.