Vindictive mother

So my mom and I have always had a rocky relationship because of her drug and alcohol abuse. Recently she told me she's afraid for how my daughter is going to grow up and I found out today she called me a psycho bitch to my Gma because I kicked her out of my house and then said she thinks I'm going to shake my baby. I'm a navy veteran, worked in the medical field for eight years now and am the god mother to two beautiful little boys. I lost a baby last year and I am already in love with my daughter and she isn't even here yet. Am I wrong to completely cut this woman out of my life and not let her see my child? I feel like I can't be around her without wanting to hit her after that.