I expect all of the kids to help. Even Dex. He hates cleaning. I get that. It's not fun. But autism doesn't get you out of responsibilities. I just make it work for him. Dex needs to see progress, not look at the big picture, and have a list. He's great at picking up, loading and unloading the dishwasher, running things around the house, wiping things, organizing things, and taking care of the dogs.
To make the day manageable, I do a couple of things. First, I add things to his list three tasks at a time. A huge list is overwhelming. I make sure they are small jobs. I'd never say, "clean your room." That's too much. He will clean his entire room, bit by bit. Same work, given differently. I also make sure there are jobs in there that he enjoys like giving the dogs treats and we build in breaks. When he's starting to get annoyed, we take a 30-minute break. He's about to take one after an hour of work. I'm happy with that. And lastly, headphones. Cleaning is loud. He hates the noise of things moving, vacuuming and carpet cleaners.
The good- rather than fighting his brain, I try to find ways to work with it. Make this jobs rewarding and productive. And manageable.