Thanks for your reply.
Irrespective of the powers of embassies, the UK and the USA are both signatories to the Hague Convention, which deals with the situation where one parent seeks to take a child out of the country, in defiance of a court order stating where the child should live.
It's a complicated issue but, in essence, both the UK and the USA agree to abide by the decisions of a court in either country. That means that, if a UK court was to decide that your granddaughter should live with her mother, in the UK, (and her father was to take her to the USA) a US court would respect the order of the UK court and ensure that your granddaughter was returned to the UK. (Of course, it works the other way round too. A UK court would have to respect the decision of a US court).
As I've stated, it's a very complicated matter but the same rules apply irrespective of which passport your granddaughter holds (or whether she has both passports or no passport at all; she's still a citizen of both countries, even without a passport). There's far more detail about the issue here:
http://www.reunite.org/page.php?alias=abroad00
Chris