My Daughter who was born in China cannot get visa to see her Chinese mother.

My Daughter was born in China. My wife is a PRC citizen. I am an American Citizen. My daughter received American citizenship at the US consulate in Guangzhou. Now i am told my daughter cannot get a visa to China because she is not recognized as an American citizen since her mother does not have a residence card in America. My wife is trapped in China and My daughter is trapped in America. They have not seen each other for 1 year. Does she need a travel document? I have read no case like this on the internet.