I signed the birth certificate of my daughter when she was born without verifying paternity. Now, 2 years later, her mother had made numerous statements that lead me to believe that I was not the only possible candidate for paternity. We have never been a family and I have paid child support and daycare from the beginning. Her mother has moved her to a new state and I have no contact with her, and it does not look like things will get better. Is there any way that I can legally force the mother to submit our daughter to a DNA test now? Just so that I know for sure what I am fighting for, before I take my next step.

It will depend on your location. In most states you should be able to ( if you are in the US. You will need an attorney and file in family court to ask for the test