So what would happen if you announced to DH that things need to be 50/50 from now on?
He collects from school, cooks dinner, does bath & bedtime 2 nights a week. (You can stay late at work, go to gym, see a movie, have dinner with friend, go to gallery, do you tube yoga in park, sit in the car on drive in blissful peace - whatever. Don't go through front door until at least 10pm).
Every other Saturday is now your day. If his regular commitments are immovable, you get all day Sunday instead. The pushback on 'Sunday is family time' is... so is Saturday, but I've been doing them on my own for 10 years now. We can either do both days together, one day each, or half and half - which is it?
If you go for every other Saturday each, ensure family Sunday is also 50/50. One of you cooks every other week. One cleans every other week. One does laundry every other week. One does shopping every other week. One does whinging about homework/playing board games/bowling cricket, whatever...EVERY OTHER WEEK.
I've not seen any explanation for why he seems quite so entitled. Does he earn substantially more than you and somehow feel he has 'earned' more time off? I appreciate that with an ASD DC1 it must be hard if he has formed a stronger attachment with you and you ease the path through after school time, winding down for bed etc.
But like some of my friends' husbands who got away with being incompetent during the toddler stage, he is just coasting through without even realising how much effort it all IS!
Book the BH weekend away with an old friend/parent/travelodge in a city with nice art galleries. Just announce it. "I'm cashing in Saturday the 5/12/19 from January in 2013. You had those 3 days to yourself, I'm having the bank holiday weekend to myself - make sure you let whoever you usually see on a Saturday know that you'll be unavailable 29th May because you'll be parenting your children.
June will open with a mindset shift, if nothing else. Hopefully a little more appreciation of how much life load you pick up. Make sure he doesn't just notice and appreciate it, but actually SHARES it from now on.
I don't lean to the LTB suggestion, but if he doesn't appreciate you more with a 50/50 split while sharing a house and a life, you might as well at least take half his earnings to get on with it yourself. At least you could afford a babysitter a couple of times a month then. And you'd have 2 weekends a month to yourself. That's not the aim, but it looks better than what you've got now from where I'm sitting.
Time to drop the ball - he'll realise how heavy it is by the time he's picked it up and run around with it for a few weeks!