How can I possibly act normal around my mother?

I grew up with an extremely abusive (physically and emotionally) mother who was constantly sleeping around and either drunk or high. I was forced to grow up fast and rely on myself. In recent years my mother has grown exponentially. She no longer has an addiction, or is abusive. She loves herself and has a fiance and a family. But she also wants to try and reconnect with me, she wants to try and be my mother. I thought this was a good thing, but when I'm with her, or hear her voice I just can't help to be brought back to what she's done. And I don't want to interfere in her new life. I'm not sure what to do, because she's finally ready to be my mother, but I'm not sure I'm ready to be her daughter. I know it's not fair to keep avoiding her, but I don't want to tell her that she was basically a bad mom. She knows she's done terrible things and I don't want her to have to relive the memories as well. How should I approach this? How do I tell her I'm just not ready without making things painful?
How can I possibly act normal around my mother?
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