Actually, she could. As I understand it, there was a time window after he reached majority when Obama could have voided the renunciation, but he did not. And that time window has long since past.
Bingo! That’s It!
Your mistaken. U.S. citizenship is, quite rightly, one of the most precious possessions we have. And U.S. law makes it clear that citizenship can be lost only if the citizen himself gives it up. It cannot be done for you, and can only be done by you if you're an adult. So Obama would have to give it up when he was 18, not reclaim it. And he can only give it up through deliberate actions. The Supreme Court has ruled that someone cannot lose their citizenship by accident. The act must be deliberate and done with the full knowledge that the person is giving up their citizenship as a result.
See #173. A renunciation has to be voluntary, and can’t be made on someone else’s behalf, according to the State Department.