Do I tell my boyfriend his ex keeps messaging me

I've been with my boyfriend 8 months and finally met his daughter Charlotte. I don't know how his ex found out about me but she did and told me "Girl I would get out of I were you. He will leave you with two teeth missing." She send me his DV charge which I already knew about. He had told me on our 4th date about his one and only domestic violence charge and he admits he lost it and punched her. I know that may seem like a reason to run but why he did it was over his daughter and as someone who had 8 miscarriages I would harm anyone who hurt my baby. Charlotte is 13. When she was 6 and my boyfriend was with his ex, she got severely drunk while he was at work and he came home to Charlotte screaming. The ex had thrown hot oil on Charlotte. There was some argument that had and she was really intoxicated when she did it. He said he blacked out. He did get a DV charge because what he did didn't count as self defense. She got felony child abuse charge. I've met Charlotte and the burn is really noticeable. She lives with her dad because her mom(not the ex gf) bailed on her and she gets bullied at school and the kids all call her Shireen instead of Charlotte. If you've seen Game of Thrones you get the "joke". Shireen had something wrong with her face. I blocked the ex but she had messaged me on 3 other social media. Should I tell him or just keep blocking