I'm still owed about 30 g's in back support and one of my kids in almost 30. I had full physical and legal custody of my two kids. I caused so much flack when my ex was not paying that I managed to get a conference call between the state child support people and my Senator's office. It lit a fire under the child support people.
Yes, fight it. If you have custody then it sounds like she owes you back support.