"when he is sober he is the loveliest man and would never dream of hurting me."
He knows what he's like when he's drunk because you've told him.
He is sober when he has the first drink.
So, I'm afraid he's not the loveliest man when he's sober as he's doing something which he knows really hurts you.
It took me years to work that one out BTW. (I'm ashamed to say I've had not just one but two relationships with dysfunctional alcoholics. What a fucking waste of my life they were).
I don't know what insanity it is in us which puts up with this crap. From the outside it is obvious to everyone that this man is taking out his problems on you, he won't change, you can't help him, staying with him is damaging you and your DD and you must get away from him.
It will be obvious to you too with hindsight, I promise you.
You need to find a way to see this relationship for what it is. Forget this "if he was ill I'd look after him" crap. Would you ever treat him the way he's treating you? And your DD? No, you wouldn't. And more to the point would he take it? I doubt it.
You can't help him. You must put your DD first. She needs a safe home environment with a happy mum, not a mum walking on eggshells in case she incites the temper (verbal or physical) of this completely unreasonable excuse for a man.
You are in danger where you are. Not just physically, but emotionally too.
Although my alcoholic exes are in the past, some of the effects of those years are still with me. He is damaging your self esteem, I'm sorry you're in this situation, it's shitty, but you have to get out.
Hitting you is inexcusable. Please, please leave.