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Your daughter's mom obviously lied about your living arrangement to get on welfare.
You may file Motion for termination of the Child Support Order and tell the Court your reasons: you are currently living with your daughter's mother and are paying household expenses. You may also inform Welfare department that she lives with you and you are providing for the family. Doing this, informing the welfare department about your living situation may get her in deep trouble. She could be charged with welfare fraud.