Right, so for a start he's a DP, not a DH.
So effectively, you are financially separate in the eyes of the law.
Whose name are the debts in? - that seems to be the biggest problem.
If his - you can forget the debts.
If yours, or joint - go and talk to CAB (or perhaps wait for other advice on here) on whether you can extricate yourself from them.
The house: how much is paid off? Is there any equity?
Because if you have no equity OR the amount paid off is negligible, then you could be far far better off cutting your losses completely - as in, moving out with the children to rented, and telling him to either cover the mortgage himself or put the house on the market, because you don't care if it gets repossessed.
So to move on to affordability on your own.
Firstly, could you get any help from family, eg to get a deposit down for rented, or some contribution to help start again?
Could you move in with family temporarily?
Is rented AT ALL affordable? - it should be if you are a single parent - HB, tax credits etc - again, go to CAB, set out the situation and ask for advice. Obviously, you would go on the list for social housing. But effectively at first you are looking at pricing up a rented home - how many bedrooms can you get away with?
Could you consider moving to a cheaper location - move job? Or to somewhere where you might be able to get family help with childcare?
CSA claim, remember.
Sounds odd probably but right now on mat leave you have more time to do this - you don't have to fit in work too. So think about taking action now.
Then work. Assume he will do no childcare. What are your hours? Could they be flexed in any way? How good is your employer? Now might be the time to talk about how to fit best with childcare to earn the most money.
Above all, remember that this will be the hardest time - you've got preschoolers. In five years, with them all in school, you could be:
a - Still sitting in the shit, looking with pure hatred at the pig you mop up after as well as doing everything for your children, watching them learning how to be layabouts and how to treat you as a domestic slave. Still servicing the massive mortgage that's doing nothing except tie you even more to him, as every year that passes makes it harder to cut the losses. Being miserable. Watching debts grow thanks to him.
b - Be waving last DC off to school, and looking forward to upping your hours and seeing childcare bills fall at last. Looking forward to seeing the small pot of savings you now have (amazing how feeding one less and not paying for an expensive hobby makes such a difference!) start growing faster. Making plans to move somewhere a bit bigger/grow that house deposit. Feeling happier and in control. Satisfied that the children are seeing a good example. ENJOYING LIFE. Looking forward to meeting someone new, if you haven't already. Running your own ship.
Yes, leaving would be hard. But impossible? It's never really impossible. Which future would you rather have?