You might not like this thought, but have you considered that by allowing yourself to be involved to this level, you're actually behaving as though you are still his wife?
He won't ever be able to comprehend or accept it's over when you're doing everything a wife/somebody who will eventually take him back would do - like sorting out tax, shopping, laundry, for example. (and having him in your house each week/engaging in messaging in between, etc). Every engagement is telling him that you're still interested/care/could be persuaded to change your mind. Including when he hears that you've been in touch with his GP about his welfare - it'll just confirm to him that you care and that means he just has to carry on and you'll take him back.
Maybe it's time to be brutal? Not respond to any messages, not open the door to him, not give him help with anything at all. Because you aren't with him anymore. Because he was abusive and accused you of being criminally abusive to your child to the extent that a) they didn't get the assessment they needed and b) could have seen the child taken into care or at the very least, the subject of a Social Services investigation.
As it is, he's obviously a potential risk to the child in such an unstable mental state and issuing threats, so there's nothing to be gained for the child from being subjected to somebody like that, especially when they've done the things you describe.
He is not your problem. You aren't together. If he actually means to kill himself, he'll do it whatever you say - but it sounds more like he is using it as a way of keeping you, especially as he's making excuses not to do anything about it.
I've heard so many different methods of suicide described by an absolute leech - incredibly specific in method. Lots of messages and voicemails sent in the dead of night saying he was just about to do x and was saying goodbye. I witnessed him engineer a situation where he could pretend to attempt suicide in front of me, convinced I'd take him back to the extent that he'd loaded up his car, brought his stuff over and told his Mum he wasn't coming back (which considering I'd never let him move in in the first place when we were together, was one hell of a leap).
He finally got the idea at that point, because whilst ejecting him from the premises, I told him how to do it properly and that he wasn't going to do it over my new laminate.
OK, I then had another six months of 'we should meet for closure', 'how are you', cryptic messages that hinted that something awful had happened to a family member, but eventually it tailed off into a yearly thing and just before I got a new phone that allowed me to block the twat's number at last, there was a 'Happy New Year Darling, how would you like to meet up for coffee today? I'm parked outside your house right now and I can see you're awake' message left at 3am.
Seven years later, he's still very much alive. Because he had no intention of ever killing himself, it was all lies to try and coerce me into taking him back because he 'couldn't live without' me his intended mealticket