Received A Child Support Civil Summons When I Am Not The Father

Last month, I did receive a letter from DSS about this lady from 4hrs away asking for child support. Me and my wife looked up the lady's name on Facebook and found the father in some of her pictures. We have the same name. I called the agent handling the case, answer all the questions and told her that after I travel 4 hrs to do DNA and it's proven to be negative, we will sue a civil case to the mother of the child for the time, effort and everything we'll go through. Agent said she will talk to the mother and will get back with me, she never did. Today, we got served and has to appear to the hearing. Question is: Me and my wife will go to the hearing, we will need to stay in a hotel up there, we will have to call off work, once proven that I am not the father, can I sue her, get them to pay for my lawyer fees, inconvenience fees, all the out of pocket expenses on doing the trip, the unpaid time off work?