I'm sorry OP, but 'feeling bad' for the kids is not a 'reason' to put up with this abusive man.
I call him 'abusive' because what else would you call a man who ignores his partners pain and distress, and deliberately adds to it by forcing her to do all the housework and childcare ? Could you watch him suffer like that ?
My guess is no, you couldn't ! So exactly why would you think it would be better for your kids to watch you suffer, every single day, and to grow up thinking that it's perfectly fine to treat your partner like that ? Rather than them have the 'upset' of separating from him, which will be over in a relatively short time ?
It's not your problem that he has nowhere to go to, that's a problem for him to solve ! (And he could solve it by getting a bloody job and paying his own way!)
You are not responsible for 'taking care' of him ! He's an adult !
(Remember, he's choosing to watch you suffer because he'd rather lie in bed and do fuck all !)
Also, your kids are going to bed early right now, so you can go to bed early too, but very soon they'll be bigger and staying up later, so your day is only going to get longer and harder !
If you keep doing what you're doing now, you'll end up being unable to cope anymore, and what will happen then ? He won't suddenly grow a conscience, will he ? No. What he'll probably do is to leave you, for someone else who is able to 'take care' of him ! Because he's selfish, lazy and self absorbed. He'll never go back to work again if he can find any way to avoid it !
Get rid of him now, to save you and your DC from a hellish future...