I have actually been in this situation with my ex-girlfriend and daughter, and my position seems to have played in my favor greatly. My child's mother repeatedly downgraded me and criticized everything I did, and regularly talked me down in front of my daughter, who at the time seemed to believe everything she was told about me, mostly because she lived with her mother and naturally sided with her. Through the year or year and a half that it went on I kept my cool. When my daughter would come around I would never say bad things about her mother, but rather share the memories of good times. When she would mention something bad that her mother had said about me I would ask her to question it, for example, I was made out to be abusive and a thief; I would ask her, "Do I beat on you or my new girlfriend?" "Have you ever seen me hit a girl?" "Have you ever seen me steal?" "Don't you see me pay for things?" "Have you ever seen me do this?" Instead of being negative about her mother and the situation, I recommend that you continue to be positive and do things that would question the mom's credibility. Show your child the positive and mature side of you and be sure not to down talk the mom. It will take time but if you continually show the child that you are not that person, without calling mom a liar, I am confident this will be overcome.