It sounds like a horrible situation for you OP. Scary and exhausting.
Are you friendly with his parents? Could you speak to his mum (since his dad is recently bereaved) and ask if he has ever had spells like this before or if it is something she recognises from her other son? Ask her for some support/to get involved? You shouldn't have to carry this all on your own. From my total inexperienced POV (apart from having a BIL who occasionally has psychotic episodes when he goes off his meds) it does sound like he is tipping over into quite a concerning state. Whether that's psychotic, schizophrenic, or very profound depression, needs assessing. But you can't do that, and shouldn't have to be living with any of it without seeking support.
I would stop trying to have it out with him for now or trying to get him to shape up - if as you say he hasn't done so for all these years, the middle of a crisis is the worst time to begin. Try not to engage with him at all. Avoid reacting to the provoking things he's saying and doing. Have a few stock phrases lined up you can turn to which are non-confrontational and difficult to argue with: "I'm sorry you are feeling that way"; "I don't want you to be unhappy"; "death is frightening". Don't try to buck him up or make him feel better because it seems precisely that is what's antagonising him into feeling so 'alone in this marriage'.
None of the above is because you are wrong to expect him to contribute, be kind, and be rational about this very natural death and death in general - it's because he's currently in a totally irrational, combative state and it won't get you anything but more grief. For now, just try to minimise the extent to which he can fuck up your day while you try and find a solution.
I completely understand why you're reluctant to break up due to the effect on the kids. But in the first instance, you don't have to let him have unsupervised contact without a court order in place - you can arrange for them to spend time together at the grandparents', say. As long as you can ensure against him making off with them, before there is a court order for contact, you both have the legal right to keep the children away from each other, it's just a question of securing control in the first instance. He can then take it to court if he wants unsupervised contact, at which point you can make the point that he has no experience of seeing to their needs as you've been doing it all, is currently depressed and anxious and behaving erratically, and move for contact to be supervised until these issues are addressed. From what you say, he may not move for contact at all, as he is both going through a MH crisis and utterly self-absorbed anyway. Using the family court to punish a spouse for leaving via the kids is the behaviour of a manipulator rather than someone in the grip of a mental health crisis - it's a complex, tedious and administrative process - so at very least this would give you clarification on what kind of beast you're dealing with here.
Take care of yourself OP. I think this situation has been escalating over time (and was probably never wonderful to begin with) so it's hard to see the wood for the trees. This is why you need to get it out there for impartial/wider discussion - talk to his family, to yours, to friends, to professionals. Posting here was a good first step. You need other people to get involved with this, it's not betraying him, it's the only way he'll ever get the help he needs and it's the only way to keep you and your children safe.
I know we don't have the full details of the Epsom College case yet, but men can and do commit family destruction when they feel there is nothing to live for. God knows why they can't just off themselves quietly like women do, but a certain kind of man has to externalise his misery as rage and it sounds like your husband may be one such man, given he seems to be blaming you for not being able to magically shield him from all the exigencies of life and death that he does not feel equipped to cope with. I'm certain if you asked Emma Pattison before her death whether her husband, whatever his problems and their issues, would kill her and their little child, she would have said no, never. As Germaine Greer said, "“Women have very little idea of how much men hate them." What you're seeing and feeling could well be the tip of the iceberg. Take action now to make you all safe.