You said that you don't think you could get much help because of your income, but I think you'd be surprised. Check entitledto.org (or co.uk?), see what you can claim if you were on your own. There is help with nursery costs if you work over 16h and also working tax credits that you might be entitled to.
It seems to me that your H hasn't dealt well with the pregnancy / maternity period. My first was a challenging baby and I remember the lack of sleep was horrible. It's a form of torture (literally). It looks as if he's already fantasising about all these opportunities, maybe even flirting, which is what is keeping him out of the house. He has not realised that the"you" who he married is still under layers of tiredness and is not helping you get back on your feet. Not only that, he dismisses your health, your feelings, your children's needs and his role as father. I'd kick him out. There's financial support available, you don't need him for that, you have a salary and maybe you will need to be a lot more tight with money but you'll get along. Consider an au-pair, if you have the room, much cheaper than nursery. I have friends who have done that.
Also, having a H like that at home only puts more pressure and work on yourself. You probably have to cook big meals when you could just go with sandwiches sometimes, all the extra wash, ironing, tidying after... you might even put pressure on yourself to get the flat clean and ready for when he's back. Not saying you don't need to live in a clean and tidy house, but I know that there are days when my DD had not slept at all that I couldn't really function, it's best if you concentrate in getting things ready for the kids, rest when they rest and leave housework and meals for when one is able to do bits. Easier without a nagging H saying how he works all day and comes back to toys on the floor and a wife in pyjamas... as if working 35h a week could be compared to 24/7 childcare duties (esp. with a child that doesn't sleep).
By the way, check your DS ears, it might be that. Does she sleep when she's a bit upright (e.g. stroller, carrier) but not on her back? Could be reflux but also ear pain.
Good luck! There's light outside. And lots of nice men who would be happy to share responsibilities, there is probably one for you down the line, if you want to.