Wrong for not trusting my own mom?

I feel a little bad but I don't trust my mom when it comes to my daughter. I have a newborn and my mom really loves her and I'm thankful for that but I won't allow her to watch my child until she's at least five. Let me explain. Growing up my mom had a really bad temper. She would get really violent with me and my sister. I have three younger sisters and the last two she wasn't as bad but she was terrible with me and my sister who's just under me. She used to shake us when we were little and quickly lost her temper on us. One time when I was 6 or 7 she was helping me with my school work and I couldn't figure it out so she got really upset, grabbed me by my neck, shook me, and threw me to the floor. I still get tears in eyes when I think about that day. She always cussed at us and she still has a bad habit of cussing at my younger sisters. I moved out when I was I 14 to live with my grandparents and it was the best decision ever. I know my mom loves my daughter and I feel bad for feeling this way because she's done a lot for her. She even brought her a stroller. My mom can visit my daughter but when she ask to babysit and I know she will soon I will tell her "no" and explain to her why. Am I wrong for that? I just want to protect my baby.