Why should I have to pay child-support?

I have 2 children with this girl I met in high-school. I have always had trouble with her paying child support, my kids are gna be 17&18 yrs. this yr! recently an officer came to my door serving me with child support papers with another child. Now, she is saying that i have another child with her! she has someone else last name, and made him believe he was the father! I got a post card in the mail from a lawyer, so i went to go see her and she told me that she could not do anything for me until I took a paternity test! So, I did, and well the little girl turned out to be my child. I went back to the lawyer and since the 13yr. child was mine, she cannot do anything for me! Why should I have to pay the mother child support when she had someone else believe he was the father! and everytime I took her to court for the other two, if she wanted to she would show up and if she didn't want to, she did't! what can I do? I know its not this childs fault, but I don't think this is right! Is there anything I can do? or is she gonna get away with this!