My ex is demanding parenting time with 2 yr. old he has not seen in months.?

He has an alcohol problem, is verbally and physically abusive to his mother and was to myself. He has a son that is 1 yr. younger than my child with another woman that he refused to even sign the birth certificate and has no interest in seeing? He has been forced to pay child support and his mother wanted me to sign and have notarized a paper she wrote up that stated we had joint custody so, he would never have to pay support. I have never allowed him to have her alone and feel uncomfortable doing so. I am concerned about my child's safety and don't know what to do? He has petitioned the court for a mediation to get parenting time and I need to know what to do and say?