Paternity Question!!!!!!1?

If someone hired a lawyer to request a DNA paternity test, will it cost the petitioner more money to take it to court and get a court order if the person will not submit to one? Is there usually a "set fee" for the process either way or is it more to take things to court? I have an abusive ex who has been haring me to take a DNA test. He knows it's not his but is just trying to get me upset because he gets no reaction from me otherwise. And I know it would be easier to just give in because I know it's not his...But I don't think that he deserves the easy way out of this. Serious answers only please. And yes, I am aware of the fact that I will have to submit to one if he gets a court order. I just want to know if dragging this out will cost him more? For getting a pregnant woman this upset he deserves it!