Can I sue the government?

When my daughter was born my girlfriend use my middle name and not my first name, now that I'm trying to get custody of my daughter I can't get anything because of my name not been correct in her birth certificate. I try getting corrected in civil court but they need my ex girlfriend signature but she has been out of the country for more than 9 years with my daughter.Civil court send me to family court but they also can't do nothing. The only answer I got at the vital records office in Manhattan was that it wasn't their fault that I have not daughter now.