I agree with 'Catza' that you should stop telling your daughter that he loves her, he doesn't, he loves the booze above everything else! Anyone who would put drinking before their child when they have been hospitalised, obviously has an alcohol problem, and your daughter is MUCH better off without an alcoholic in her life. Just agree with her when she says she is sad about his drinking. Tell her that it is sad, but he is an alcoholic, and the only person who can help him, is himself, as he needs to admit that he has a drink problem, and then seek help but he will likely only do that once he's hit rock bottom.
Meanwhile, stop thinking that you have a duty to make him happy, when to make him happy, means that you have to do everything he tells you to do, and when he says jump, you have to ask how high. This is no way to live OP, and certainly not a way of living that your daughter needs!!
Let him go, get advice from Women's Aid, and show your daughter what a happy home can be like.
Oh, and as for him taking the overdose because he thought you were out with other men, that's likely to be judging you by his own standards, ie, if he's out and away from you, he's probably screwing around, which is why his mind immediately jumps to you doing the same thing! Also, what did he think you were doing with your daughter, while you were out with these other men? The whole thing was a ridiculous ploy to frighten you, and make you do exactly what he wants you to do. Emotional blackmail is cruel, and is NOT something you should allow yourself to be controlled by, or you will live in fear for the rest of your life.