Thank you for that additional info. I understand what you are saying about your daughter, but somehow you have to face the fact, that up to this point, you have failed her. At three years old, she is literally a sponge, soaking up her environment and learning the abc's of life. She looks at the relationships that are shared between you and her, her and your mother, you and your man, your man and your mother, her and your man, you and your mother and so on. It's family dynamics, and parts of it can stick with her for the rest of her life. Women who witness domestic violence as a child are far more likely to grow up and be abused, or to become abusers themselves. You are being abused, but you are also abusing your child by keeping her in this situation.
If that's not enough to have you want to leave right away, consider the fact that he's already put his hands on you, he's already almost killed you, and the next time he may not stop, the next time could be your last breath and then where will your daughter be? Worse case scenario, he takes your daughter, and she never knows what a beautiful, sensitive, and smart mom she had, all she will remember is the violence.
There are many, many opportunities available to a woman who is being abused....and thats what this boils down to, you are being abused. No one can tell you to take that first step to get out of this situation. Ideally, the next time he puts his hands on you, you call the police and have him arrested. This way he will be locked up and it will give you a chance to get things together and decide what you want to do while he's locked up. When he does get arrested, you'll want to file a restraining order so that he cannot come near you or your family. You can contact domestic violence services online or in your town. If you give me your city/state/county, I will look up resources in your area.
Only you can make the decision, but you need to make the right one, if not for yourself, for your daughter, who is too young to understand whats going on, and too young to defend her body and mind against the things around her. Thats your job.
I welcome your thoughts, let me know if you want to talk more.