I don't believe the United States recognizes "dual citizenship" per se.
Now, that's not to say that you can't be a citizen of American and also recognized by another country as a citizen of that country.
My husband was Canadian until he was naturalized. Our son technically has dual citizenship in the eyes of the Canadian government, but not in the eyes of the American government.
At least that's how I understand it.
Here's a link talking about it.
http://www.us-immigration.com/information/dual_citizenship.html
When you are natuaralized as an American citizen, you renounce allegiance to any other government.
The U.S. considers you are only an American at that point.
(Other governments might ignore this, but a natualized citizen is only an American.)
A president must be American-born. Of course, there is no restriction on a "first lady" being foreign-born.
I have friends in Texas that are both Mexican and American Citizens. Weird...I don't understand it.
Besides, the Mozambique that Teresa was born in bears no resemblance to what it has become. I would doubt if it would recognize any claim she had to Moz. citizenship if she were to maintain one.