OP - I've been where you are, in terms of having an emotionally abusive mother (because that's what your mum is). My mother was an emotionally abusive narcissist.
During my first year of primary school, she had left home for five years, and my brothers & I didn't see or hear from her in that time. For reasons I don't know, my parents didn't divorce in that time, I guess because my dad didn't know where she was. As a result, she crawled back, and dad agreed to give it another go. This was the catalyst for our bad relationship, because when she returned, she was virtually a stranger to me (and I to her). She would constantly put me down, made me feel worthless, and told me that my dad felt the same but was too afraid to tell me. That's why I didn't' tell my dad about it, because I was terrified about what he'd say, scared he'd confirm he felt the same.
When I was 13, we relocated to the U.S. (my mother was American), and her emotional abuse got worse. Then she left again, to be with another man, and the truth came out. My dad was horrified. I started therapy, which I still have to this day, although not as often as I did back then.
My mother (I refuse to call her mom) died last year, and just a few weeks later, I discovered I was expecting my first child. And like you, when I found out I was having a girl, I was upset. And bloody petrified. Me? A daughter? But what if...?
My DD is four weeks old, and the moment I laid eyes on her, all those fears melted away. All I felt was unconditional love. And it hit me, that I know I will never become my mother, because from her I had a masterclass in how NOT to do. If I have to say one positive thing about my mother, it would be that, that she's shown me how not to be a mother. (She wasn't a great mother to my brothers either).
I can't tell you not to feel the way you do, because I understand why you do, and would go as far as to say it's perfectly natural given what you've been through.
However I feel confident that like me, once you see your DD, you'll realize that you could NEVER be like your mum, because like mine, she's an advert for how not to do it.
Finally, I would say the very fact you're worried/fearful, is a clear sign that you will NOT be like her. You are already thinking of your DD's welfare.