Oh OP. This is such a common experience. The husband thinks that it's the wife's choice to work, and that her rightful place is at home, being a 1950s housewife and housekeeper.
These are things that should be discussed and agreed to before marriage. I don't think a traditional set-up is all bad, but I do think that many men aren't honest regarding how attractive the 1950s pipe & slippers marriage is to them.....if they were, I'm not sure if their wives would have had children with them. Others change over time as they realise that this kind of set-up suits them fair better than the more modern marriage.
I understand that if he earns a lot more than you, he might think it's pointless for you to work, but it's also pretty important for you to keep something on your C.V, even if it's 1 day a week. Employers frequently don't even ask how many hours you worked in your old job. They just see a job, and if you were ever in a vulnerable position, that job could make the difference in you being able to hop into a full time position elsewhere instead of there being a massive gap in your employment. If he's purely thinking about his own needs at the expense of yours, it's clear that it's simply not in his interest to have a wife that has as much independence and ability to leave as he does.
Which brings me to my next point - wife. I note that you say your his partner. Why am I not fucking surprised? Permit me to make an assumption here, and assume that this was his decision? Either you wanted to get married or weren't bothered, but he either never asked or made it clear it was just a piece of paper of some other poor excuse?
If that's true then I can see very clearly what's happened here. He's set up a pretty good situation for himself, hasn't he? I assume the kids weren't an accident? If they weren't, then he's managed to bag himself a girlfriend who stayed and actually had babies with him. He sounds like he would quite like a wifey at home - but without the fucking marital protections for you. Do you have separate bank accounts? Any that are joint? Do you at least own your home together?
He puts the children to bed most nights, bath and bed routine.
That's good. It's a start, but doesn't make up for gaming until 3am. That's just beyond. Where your cuddle time together? Where the intimacy here. He just shuts himself away. You must be lonely :(
I have said to him that if he lived alone he would have to do more than he does now, just as the basics of adult living. His response was well he’ll move out then
He knows he holds the ace card here OP. He knows he has the financial power, so he won't budge an inch if it doesn't suit him.
If this is what he's like when you have a job, I think he'll probably get worse. You can tell what a person is really like inside when they think they've got the upperhand.
Do you like what you've seen so far?? If not, don't even think about giving up your job.