You're EXTREMELY vulnerable as an unmarried sahm with NO claim on your home!
Was this child planned?
You ARE contributing to HIS mortgage - albeit indirectly - and getting NOTHING in return! The money YOU are spending out of your savings to cover the JOINT child's costs, to cover your reduced income from being on Mat leave is freeing up HIS money to be spent on HIS mortgage for HIS house that you have absolutely no claim on! How much per month are you paying for the child's costs? Half of that is what HE should be paying, I'd argue he's also half responsible for however much your income is currently reduced by - how much is that? How does the total of those anounts compare to what he's overpaying HIS mortgage by? I'm guessing a good chunk if not all of it, so actually YOU are overpaying the mortgage on a house you've got ZERO claim on!
If you tell us:
How much is his monthly income
How much is yours
What your total household outgoings - including your (JOINT) child's costs are
We can advise on a fair setup.
"What's fair is your name goes on the mortgage all money is put in one pot all bills go out of one pot (including childminder) and what's left is split." Actually this is a very simple way to do things fairly!
Certainly doesn't sound fair at the moment!
He definitely is half responsible for childcare fees - that's his child and his responsibility too.
"He sees it as him paying it off for OUR future." Oh really?! Then he can put your name on the deeds then! And make a will with you as beneficiary - at the very very least! Although I suspect this is him spinning you a line!
"He has also offered for me to quit work on numerous occasions and that he would.support us so he isn't being a total shit. He just assumes we will never split up." Or he KNOWS if you split all you could pursue him for is pitifully low and poorly enforced cm!
"I don't think we will get married. We completely disagree on the type of wedding we want so it won't happen. He wants a proper celebration with everyone there. I would want to elope." Then you compromise with a smallish wedding - though quite honestly you both need to realise (I suspect he already does! And is using the idea of a "proper" expensive wedding as a way to put you off) that weddings and marriages are different things. Would be very interesting if you were to call his bluff and go "ok we'll have the 'proper' wedding you want - in 6 months/a year" cos it's possible and doesn't need to be expensive, but I'd bet good money he'll then come up with more excuses!
"Does anyone know what would happen if he died?"
In the most extreme eventuality if he dies - you're basically screwed! You have NO claim on the home so you'd probably have to move out, you wouldn't be able to claim any of the benefits that can help out at such a time, if he has his own bank accounts they'd be frozen and you wouldn't have access to that money. You'd likely be homeless, potless and with yourself and a child to see to, plus possibly a funeral to pay for (if there's no other family, if there is you may get NO say in the funeral you might even be prevented from attending)
Worse if no will but a will doesn't massively improve things as his family (parents, siblings) have the right to challenge it and most challenges are successful.
I've actually seen this happen to a relative, completely screwed over by not being married to partner, who died unexpectedly and quite young.
"I assume everything would go to our baby but what would happen to the mortgage would I be able to continue to pay it and then it goes to DC when 18???" Assumption is a HUGE mistake. Which part of the U.K. Are you in? The laws vary. England and Wales, Scotland and Northern Ireland all have different rules on inheritance.
Even if you "just" separated you have no more rights than a lodger. He can evict you no problem, with potentially very little notice pretty much on a whim and you'd have no comeback, no compensation.
Stop!
Stop subsidising HIS mortgage - he pays half child's costs and covers half your reduced income - at the VERY least
Stop accepting his excuses for not getting married
Stop being his mug! Don't let him deflect or fob off or soft soap you