I'm so sorry you've had this dumped on you.
It's passive aggression of the worst sort - he's decided to do what HE wants, to get HIS own way (or so he thinks), by placing you in an impossible position, before any attempt at discussion and/or compromise re: how you both manage 4 very young children and bring in a wage.
The worst thing is he almost certainly would NOT have done this if he was a single man on his own, because there wouldn't have been anyone else around - like you, or his parents - to pick up the pieces, and he would still have needed to put a roof over his own head. This makes what he's done, when he has 4 kids, all the more appallingly selfish. I don't give a toss about sole provider stress - though I admit it exists - when someone behaves like this. He certainly isn't thinking of his children, and the assumption that you will go back to work, aside from the fact that he's supposed to be in a partnership and therefore NOT "in charge", is bloody pie in the sky stuff at this moment in time when each vacancy is attracting 10s, or 100s, of applicants and hard pressed (or, in some cases, advantage taking) employers are offering lower wages in many sectors than they were even 6 months ago.
I really don't see what can be gained from staying with him ..... I don't see how you'd ever be able to respect or trust him again, even if you were able (and willing) to find a FT job capable of supporting you all. I would remain full of resentment forever more that he could make such a crass, selfish decision endangering the whole family's wellbeing, for the sake of him retraining (unless I've missed it - as what ? and with what ? - seeing as you say you're in debt). Added to which, if he is retraining, how is childcare for 4 children going to be paid for if he's out of the house at college most of the time ? He really has been a complete and utter shit to you.