Ok, OP, deep breaths. He is at the border between denial and bargaining.
Just a reminder:
The bargaining:
What have I done? Why can't you just explain it, then I can try to change? (this is so that you spend the rest of the day arguing about what he has or hasn't done, so by the end of the day you are exhausted, confused, and he buys time)
I can't do everything, can I? Surely you understand that? (you are the unreasonable one)
Can't you give me some time to process this?
What is it you want me to change? (putting the burden on you to define EVERY SINGLE LITTLE THING THAT NEEDS TO CHANGE so that if he, in future, does something similar, he can say that you never mentioned THAT)
What are you going to tell the kids? (meaning, YOU will have to explain to MY kids why YOU are doing this to them)
Let's ask [your child] if he wants me to leave. He won't see his siblings again, is that what you want?
If you want me to just do more around the house, spend more time with you, why don't you just say so?
What about the five years we've been together, do those years mean nothing to you?
What if I asked you to marry me? (note: he did NOT just ask you)
This is all to buy time and keep you in constant contact with him because he hasn't figured out yet how he's going to manage with three kids on his own in a tiny flat. Once he figures that out, he will stop bargaining until his next crisis (or until he meets someone else who will take on his responsibilities).
You do not need to respond to him. If you have said what you need to say now, and have what you want now, you do not need to respond to his frantic attempts to backtrack, because that's what this is.
You contact him IF you need to (admin, etc)
You are not his prop and he is not your responsibility.
He's barely giving you time to breathe, and that's part of the playbook as well. Be careful here.