"She, and her children, are in the U.S. In case you've forgotten, an American embassy is on American soil."
Now all Sarah needs to do is to stay in the Embassy for another ~2 years and she can apply for a certificate of citizenship (naturalization) for her kids. She's already got ~5 of the required total of 5 (since the kids were born after 11/13/86), but 2 of those years must be after the age of 14.