His word means shit all. Of course he won't move out of the property that he owns if you split up - he doesn't even really feel responsible for his children, let alone you! YOU ARE VULNERABLE, VERY VULNERABLE to being made homeless and broke, at his will, at any time of his choosing. You are not free to walk away from him and that makes you vulnerable as hell to dancing to his tune as the only other option for you is to risk being made homeless if you displease him. You are at his mercy - that's never a healthy thing for a relationship and you deserve better.
Here's what I BEG you to do as a matter of urgency;
- SAVE your money for yourself. Don't pay him a penny rent, and pay bills by % earnings, not 50/50.
- MAKE A PLAN for how you would leave instantly if it ever came to it, and get yourself the resources you would need - money, house, whatever. Make yourself a woman with options.
- GO TO WORK FULL TIME and he has to put up with the increased cost of childcare. BUILD YOURSELF A CAREER AND A LIFE AS IF YOU WERE SINGLE. Yes pandemic makes this harder - do it anyway, and with urgency. Same with equal division of housework. You are NOT to be his live in maid if he won't even put a ring on your finger and guarantee legally in writing that you won't be homeless and broke at his will. Fuck. That. Shit.
- Recognise that he is a Low Value Male, and stop giving more of yourself to him and this relationship than he is willing to give to you. There is a reddit thread called Female Dating Strategy that I suggest you read about LVM.
I second all of this from BillyTodd
Id add that I bet you're a nice person, who thinks the well-being of the children will suffer if you go back to work early and he has to do more (any) childcare, or also that you won't be able to afford the childcare cos he won't pay it. Yeah. No. The children will be fine and if there is any suffering it'll be minor in comparison to what you're risking here, by working less a day longer.
If he refuses to pay childcare, deduct it from what you normally give him monthly. It might be all you normally give him. As his name alone is on all bills, that's not actually your problem.
This man, who you love, is treating you horribly. The scales are so unbalanced it's actively cruel. And yet you're not alone. So many women end up in similar situations because they believe the myth sold to women that love makes up for everything abd they're lucky they have a man.
Start this evening OP. Figure out how you're going to increase your earnings and savings.