We are not married, he has one son (14) and I have no children.
He earns a bit more than me but we both earn well (though I work short contracts so if you take out when I'm not working the annual wage is less, but that is partly my choice (and partly cos he and the ex can't sort child care...)).
Are savings are like yours - I save, he doesn't. He got some money from the divorce/house equity and some from a later voluntary redundancy (and was straight to another job so didn't need to live off it).
We bought the house 50/50. I paid for my 50%, he didn't pay for all his. So, there is a mortgage (which is in joint names as the house is, so it has to be) which only he pays. I mither him constantly to bring the outstanding term down, bring down the interest rate (we've just gone onto a 5 year fix, hoping it'll be paid in that time, though the term is 9 years).
We own as tenants in common so each of us owns our actual share.
Because of this, we have life insurance on him which will pay the mortgage if he dies (as it is not my responsibility to pay for the bit of the house/his estate owns). We don't have any for me.
I have c£80k savings, he has c£0. Actually, that's not fair, he does have c£3k in an ISA and maybe £10k in premium bonds. But this wouldn't last long f he was out f work.
We both pay into the joint account, he pays more than me though we have not based this on our wage income but generally 50/50 but a bit more for him in the holiday line and the groceries line, due to his ds. There is also a savings line which is £650pm for short term savings (holidays, heating fuel, insurances, home improvements, Christmas) and £350 for long term savings. We've been doing this two years. Of that £350, £100 is for a JISA for his son which he hasn't got round to actually opening yet. But we now have got a small sum which we could live off for a few months if we needed to. He is amazed by this.
I reckon in two more years that will be our 'emergency fund' and we can start investing the new money in something more risky/with more return. Or stop paying it, keep it ourselves and put it in our own ISAs (no joint ISAs of course).
In theory this plan leaves him with more disposable than me but obviously he has massive incidental costs for ds (even after his maintenance is paid) and he's not great with money so I just leave him to it, while I quietly save.
We have a deed of trust so that if we split up the house will be dealt with in the way we agreed up front - i.e. he pays off any mortgage, or if he buys me out it is my full share, not a share of the remaining equity (i.e. that would be post mortgage, so I would get less than I put in, which is not the agreement). If the agreement wasn't there then it would look as if the mortgage gets paid first (which it always is anyway) and then we split the remains. But that's not how it will be done. The mortgage will be paid first, then I get my original 50% input, then he gets what he put in then we split any additional equity 50/50. Or we take any loss 50/50.
It is a bit of a minefield.
I think once you have children together it all changes anyway and it should be all in together. One if you will probably have reduced income for a while so the other should be putting up more money to cover that. Maybe you could agree to 'ring fence' the savings you went into the marriage with, or some of them, and then start afresh with equal contributions from there?