Any chance you can sit him down and chat with him as to what he thinks he can do, and what you can do in return.
It's hard, but i think, if he chooses housework over childcare, he will understand how hard it is amusing, caring for and being with 2 LOs. If somehow, by some miracle, you can get him to see what it would be like if he had that all day everyday, 7 days a week....
You seem to suggest that he can only manage 1 at a time, so if you talk him through it gently and sympathetically, he might just grasp what your day-to-day is like.
You DO need a break, You Do deserve it JUST as much as he does. Likewise, he needs a break and deserves it as much as you do..
Try some negotiation, try divvying up the weekend mornings for a lie in, if he needs one on the saturday, then you set everything up for him to get up for you on the sunday...
Do whatever you can the night before to make it as easy for him as poss.. otherwise he'll either not do it again, or he'll be bugging you every 5 minutes.. where's this, where's that and in the end you may as well get up!
Any chance you could get someone in on a Friday afternoon to give you a hand with getting the house ship-shape?... it'd be one little thing less for you to try to do with 2 LOs... And then the house is nice for the weekend and he won't begrudge picking a bit of stuff up etc.
If not, then try and set yourself a task list and schedule a task each day.. while they are napping perhaps? then at least you ought to be able to get it done without too much interruption. Once they are put to bed, then hopefully you'll get your chance to put your feet up.
It's rubbish, but it will get easier.