The problem is the kids. They are not American citizens.
Of course they're American citizens. Any child born to an American Citizen has citizenship rights. They'll have all the rights of a citizen until they reach the age of 18, when they have to make a choice.
The above being subject to their presence in the US, of course....
Yes, they are American citizens.
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Birth Abroad to One Citizen and One Alien Parent in Wedlock: A child born abroad to one U.S. citizen parent and one alien parent acquires U.S. citizenship at birth under Section 301(g) INA, provided the citizen parent was physically present in the U.S. for the time period required by the law applicable at the time of the child's birth. (For birth on or after November 14, 1986, a period of five years physical presence, two after the age of fourteen is required. For birth between December 24, 1952 and November 13, 1986, a period of ten years, five after the age of fourteen are required for physical presence in the U.S. to transmit U.S. citizenship to the child."
By this standard, the children of Sarah are not automatically citizens. However, in that her presence in Saudi Arabia is due to a parent/kidnap situation, the INS (or successor agency) may have some latitude in making a determination.