[chrisnj]

You said both your children are British nbc and USA nbc.
So are they loyal to Britain or to USA? or to both countries (i.e. they have divided loyalty!)?

And congratulation - one of them can be British prime minister and the other can be US president! Together they will rule the world.

[SmokingJoe]

It's not mutually exclusive. You don't have to be disloyal to America to be loyal to Britain. The two countries have been allies for decades. Britain is America's closest ally.
However, if any of them should be foolish enough to want to run for president(just kidding), they are gonna have to renounce their US citizenship, and even after that they'd be raked over the coals by birtherism. I wouldn't recommend it myself.