OK nitpickers, of course when her daughter grows up and reaches 18, she could try to move to the USA and claim citizenship there based upon her mother's nationality regardless of her own place of birth.
I meant, of course, that the daughter HAS NO CLAIM TO US NATIONALITY NOW, as a minor, unless she was born in the USA...Sweden is her only and presumptive home, and only it could issue the daughter a passport/travel document...and it would be the only legit forum with regard to the daughter and her custody, and in that nation's courts the husband would surely prevail.
crystalk says: I meant, of course, that the daughter HAS NO CLAIM TO US NATIONALITY NOW. This is not true. My daughter was born in Sweden. We got a Certificate of consular birth for her and a US passport. If you are a US Citizen and have a child born overseas GET THESE DOCUMENTS ! Remember without a US passport nobody has right to enter the US !