What can I do to get back child support reduced for the years my son lived with me?

I assume you have a written child custody/support agreement (either separate or part of your divorce agreement). You can file a counter-claim or counter-petition not only to recoup the overpayment of child support during the years your son lived with you, but you might even be able to get child support arrears from HER if you can prove your child lived with you and that you supported him during those years. If your ex was unwilling to care for your son, you can also file a petition for violation of the custody agreement  for the years your son was supposed to be living with her, as long as you did nothing to alienate your son from his mother, or discourage him from seeing her, or withhold him from her.