You seriously believe that this friend added her name by accident? And your girlfriend didn't notice the problem when she signed?
You need to help us out here - this was an application for a birth certificate (with her friend perhaps also "accidentally" marking that she was married to the mother), or an acknowledgment of paternity? If it was an acknowledgment of paternity,
which is an affidavit, how did she manage to "accidentally" convince the notary that she was a man?