OP. Ending the relationship would not be giving up, or giving in. It would be waking up.
Let's say you decide not to tell your family about the abuse and violence. Are you worried how you're going to explain why you don't want to be with this man? The only reason you need to give anyone, including yourself, is that you're not happy. That's it.
Leaving an abuser isn't entering into an on/off drama of a life. It's being clear headed, deciding what you want and doing something about it. His selfishness is astonishing. This lovely man, who sat in a hospital chair next to you (warm room, cup of tea, admiring nurses?) is now gas lighting you in a car whilst you self harm. Then stropping off to let you mull over what a naughty girl you've been. Go on, reverse the roles, let him be unhappy (believe me he so deserves to be). Turn the tables on him, call his bluff - all those other cliches. Basically decide the fantasy is over.
You haven't failed, he's failed you massively. If he can find a car and a roof over his head with some other vulnerable woman he will - be in no doubt. Walk away with your head high before he does.
Actually he won't be unhappy if you split. He's still got his money, drugs, booze, mates, your car and a sofa to surf on. He's not dreaming of tea in the garden, you're not going to be denying him anything. You don't want the same things. He wants a shitty Jeremy Kyle type life. Fine, let him have it. You want peace, safety, kindness, hope. You and your dd CAN have all this. You're the normal one, not him.