If he can't control his drinking and cant stop until he is utterly shitface or passed out then I think the Op has is more than reasonable to ask he not drink when he is in charge of their baby. Given that he can't limit himself it's not so unreasonable to think he has had more than half a can and that he has passed out due to being shit faced, esp his behaviour when he did wake. A single parent having a few drinks on an evening is fine, but regularly drinking until you're shitfaced and unable to be woken up isn't.
I can kind of relate OP as we've had same problem but with MIL. It crept up, she would have a glass of wine to relax at night , then two glasses, then three, then she would start earlier and earlier and then she moved to gin. Dh and I didn't use her for childcare for work so it wast really noticed when I said she couldn't have dd in her own as it happened rarely anyway. Sil and bil though cant work without her help, they begged her to get help, to not drink around the children, even paid for her to go to residential rehab. She's as bad now as she ever was, she on,y ever got help to keep her daughter off her back and was drinking within days of coming out.
She was also,found passed out in sofa with toddler and 5 yr old roaming around, she said it was only one drink and that the meds,p she'd been given must have reacted funny. Sil and bil were desperate for her to be ok and let her continue to look after the children. There's be enough several more incidents over the last ten years, when she does something really SN erious and family threaten to cut contact and not allow to see dc, she makes all the right noises abiut getting help, sometimes sees the go once and then family feel sorry for her at it all starts again. Addicts become very good at lying to everyone, esp those who love them.
You can't make him stop, he needs to want to stop. You didn't cause it, you can't control it and you can't cure it.
If he wanted help he'd have got it before, if you tell him you're leaving him be ready for him to put his recovery on to you, "I'll drink if you leave me" "you and dds are my life, I can't do it without you" etc, you can support him to get better but you don't have to be in a relationship with him to do that if you don't to be. You can look at things again in a year or so maybe and if he's better then look at getting back together?
If it's addiction, my concern would be that if this isn't the line that makes you leave, he may do it again or worse. Mil falling asleep on safe should have been the point where bil and sil stopped her having children unsupervised, there was so much worse to come and almost all of the grandchildren hate being around her, it's heartbreaking because Mil was one of the kindest and loveliest women.
I'm sorry OP you're going through this 