Being a woman doesn't make you the default cook, cleaner, nanny OP. Who gave you that idea?!
I love my DSC to bits and work my arse off to give them and us a great life. I don't have any of my own so the children in this house are my DHs and the work of the house is much much more than it would be for me if it was just the two of us. But it's my choice and when they're at their mums or asleep I prefer we spend our time together replaxing, not with DH alone clearing up their considerable mess or doing their laundry so these tasks are shared, whether they're here or not.
There are some meals they like that I always cook and I sometimes get up with them and we do DH breakfast in bed. However, DH has NO expectations at all and he's well aware they're his children and anything and everything I do is done willingly and as a bonus.
In the early days I definitely tried too hard and would make myself do things with them because I thought I should even when I was exhausted and would rather have been in bed reading a book or out with a friend. But looking back this was all on me and my efforts to be superstepmum.
Before we got together DH did everything for them. He's their dad. It's his job! He'd still happily do everything but I chose to be with him knowing his children would be a big part of my life, my time, my home, and I invest a lot in them and our little family. Yes, it's sometimes exhausting, no, it's not how I imagined my life, but I've found a good balance of pitching in and stepping back. Sometimes I spend hours playing shops, painting nails, baking, crafting, getting up far too early, bandaging knees, reading the same book over and over. Sometimes though when I've had a long week at work and need a bit of down time when one of them asks to do something with me I say yes but not for a few hours as I'm tired/am having a soak, am popping out, and they have some time with their dad. They're not disappointed or hurt. They know I love them and am there for them, but they have their dad and we all get to do things we want to when we need to.
I'd love DC of my own and hope it'll happen for us, but for now I don't and I get the benefits of opting for child free time, sometimes, even on the weekends! 
It sounds like your OH is opting out and failing you all really badly. It's not bloody good enough.
His children, all of them, are his responsibility. Your two are yours. How would he cope if he didn't have you to do everything for your DSC?
My DHs life as a dad is a lot easier with me around as an extra pair of hands. We make sure he has time with them alone which we all enjoy and gives me time with the other. We have two incomes, two sets of ears and hands and we all get along well. But he'd be fine, with them, without me. He was doing pretty bloody well before!
Don't let him pretend you're "rejecting" his DC by not doing everything for them and choosing to spend time focussing on your own. If you're as shattered and wiped out as you sound you won't be much good to anyone if this carries on much longer. If he's choosing to work on nights when he has them and not asking if you're happy being on sole duty then that can stop for a start. Again, what would he do if he wasn't in a relationship?
You should be a bonus, not the only parent to his DC when they're in your home.