What else is going on in your relationship, OP?
There are posters on here who have never married, have children, and all is fine.
However, they tend to have shared assets and often have sorted out what will happen in the event of death (slightly morbid but important).
The fact that assets are in his name, the fact that you say you keep raising marriage and he says no - both those make me wonder if there is an elephant in the room in your relationship.
The elephant is your perception that there is a power imbalance at the very heart of your relationship. Not just around money and assets but also around care. You care more, you own less.
And, of course, the two go together. If you care about your partner, you won't wish financial insecurity on them. If you care about your partner, you don't let them live in a situation in which they aren't able to assert themselves.
When you ask him about marriage, it's a straight-up conflict: you're asking him to prioritise your wishes above his own.
And he says no.
In fact, he refuses to even discuss or debate it. He minimises what you're telling him (it makes you unhappy and insecure not being married).
That's the opposite of caring for you.
And he's very bluntly prioritising himself and telling you - very bluntly - that he comes first.
No wonder you're worried.
So ...
Going forwards, you are going to have to prioritise yourself and your future. And, yes, that is going to sometimes cause other people some discomfort.
But, come on, you're owed that. At the moment, your whole existence is about providing comfort for others. That's no way to spend your existence.
Getting a job and childcare is something you really should do.
If it means learning to drive, do that. If it means, initially, paying out more for childcare than you earn - that's fine. You've been unpaid childcare, subsidising his assets for a while now.
And if he sees you are serious, he may well take your next attempt to have a discussion about marriage more seriously too.
It's a horrible feature of humans that they are more likely to give credence to someone in a discussion if they think the person they're talking to isn't a doormat. I wish this were not the case, and it's not true of everyone, but it's common enough for it to be worth you to get yourself in a stronger position.