majormug, one of the most painful things that I have found about having children, is having to face up to difficult decisions, that on my own, I would run away from.
You have to take everything into account, and only you can decide, but dont forget to factor in, what your dd will say to you when she is grown up.
She depends on you to look after her and protect her. She has nobody else. She is only a child once.
You haven't given a full picture of your relationship, but what you have posted is fairly shocking. Its hard for an objective outsider to see why it would be best for you to stay with a man who makes you cry because he is so harsh with your dd.
Splitting up is scarey, but there are lots of advantages as well. Just read the lone parents board, hardly anyone ever says that they wished they hadn't split up.
I stuck with my marriage for years, looking back, I cant imagine what was in my head to put up with what I did. I was in a real doormat way of thinking!
whatever you do, TAKE COURAGE, and dont make a decision based on fear.