I'm sorry for what you've just endured. Mine threatened the suicide too. They are WAY to self absorbed to do it. It is just more talking. Remember, they say and do what ever they think will work on you. They lie, and make up stories, and project their bad behavior on to you.
Stay strong. You are moving in the right direction. You can see from his actions that he has a very low chance of recovering. Rehab and AA everyday, yet still drinks. He is powerless to stop. You leaving may be the best thing to ever happen to him. He may then realize what alcohol has cost him.
The regulars are no doubt tiring of my party line. But here it is again. I should have left at the first sign of the alcohol troubles. now, 22 years later I'm still married, a whole lot poorer, and wondering why I let it happen. Think it through and make the best decision for you and your kids.
Best to you.