How do I prove and fight against false CPS reports that are used as a form of harassment against myself and my husband?

I divorced my husband in 2008, he was an alcoholic and was abusive. We have two children and I was to have them week on and off. He never paid child support or provided medical insurance as ordered per court. He also showed neglect and I eventually got granted emergency orders and temporary custody. Due to the fact that he had a lawyer and I did not, I signed a parenting agreement that I did not agree with and the judge decided to give him a chance and let the kids live with him during the school year. My new husband and I are supposed to receive the backed child support and can claim taxes on the children until his debt is paid. The judge also told him that we would not be paying him child support and that the custody is still split. We figured that we would not appeal the judges decision and see if this arrangement would allow him to straighten his life. Last week I got a call from CPS, the lady that handles are case was in front of our house while we weren't home. This is the second time she was called (the first time it was an unsubstantiated accusation of neglect, severe physical abuse, starvation of the children, you name it). The first time she came out was after I filed for the emergency orders and knew that it was my ex's girlfriend that filed the report because my ex husband was incarcerated at the time. When I questioned my ex husband on the stand about the report he admitted it was his girlfriend that filed it. his time the CPS lady told me that we are being accused of locking the children in their rooms and not feeding them for days at a time. She told me that she is taking this with a grain of salt and said she thinks these accusations are ridiculous.(Pretty much letting us know it was the same person who filed the first time) Nonetheless, we are going to be subject to yet another investigation, and another investigation on my record. I would like to know my rights on how to fight this harassment. I am currently in a legal studies program and feel that accusations like these will taint my future, i also feel that these false reports are a way of trying to fight and harass me and possibly set up a case for a future custody case for financial gain.