I’d be very very nervous.
You are not married which I am sure by now you realise was a very stupid thing to do given your situation so there’s no reason to labour the point.
He seems unpleasant (name calling, mild financial abuse “ this is MY house” and stone walling). He is clearly fastidiously ensuring you have no claim at all on the house as you are paying all standing charges not any of the mortgage. This is not a coincidence.
The half and half for the expenses is very business like (you just had a baby so are on maternity and he wants you to pay half - what a Prince
)
I would try and revisit with the “we are a team” let’s contrbute proportionally so we have the same spending money/ money to save. you should point out that your ability to earn is hindered by the childcare you do for both yourself and him!
His response will be telling - my prediction is he comes up with a load of shit excuses and insists on half half or something that leaves you worse off.
The point of this conversation is more for you to help you establish who you have made a child with and whether or not he actually gives a shit about you.
My prediction is sure as eggs is eggs in a few years you’ll want/need to get the fuck out of there. With that in mind...
-Buy nothing for the house.(repairs, paint, furniture)
-Go back to work
-Make him pay for half the childcare that’s needed or if he can be home me let him care for your child.
-Start saving everything you can - do not discuss your savings with him. Bank online and did not get statements sent through the house.
-Do not buy “extra things” for the baby outside the half and half. You will want to, but don’t, you are MUCH better off saving that £2/£5 etc
- cooking, honestly eat with the baby earlier and let him sort himself out if he won’t cook. Say you weren’t hungry and don’t wash up his pans no matter how long it takes.
- (as above) tackle the housework issue now! have a conversation now about who does what in the house (Make and agree a list) because he’ll expect you to do everything in the house, got to work FY and contribute half financially while he sits there like lord bountiful.
You’ll need all the savings you can get because this guy is a cheap fuck and he doesn’t view you as part of his team - he views you as someone out to take “his money”.
You are most likely right to stay put while the baby is small but I’d be making an exit plans