@mae88 We only have one kid, so I know it’s easier, but here’s things we’ve done.
His toys and all get cleaned up as part of the bedtime routine. We did that from the very beginning and it’s now just part of my son’s routine. He’s 9 now and he just does it without prompting most nights. He even knows that if he wants to play video games with dad after dinner that he needs to have everything cleaned up and will do it before he even asks me. He’s even gotten into the habit of cleaning up a big mess toy (like his Hot Wheel tracks) before switching to another toy because he doesn’t want to have an hour of cleanup at night before bed.
We tend to do dishes in the morning. We use the dishwasher. Run it after dinner, get the kid situated with breakfast in the morning, and then unload it while he eats.
And we started doing “Saturday chores” when my son was about 6. Before that it was hit or miss whether things got done unless we were having company. But we have a list of chores like sweep the kitchen, vacuum, clean bathrooms, dust the living room, etc that are just the things that need to be done every week. My son is expected to do two things on that list on Saturdays before he can get any screen time (and if he skips it on Saturday, he loses screen time on Sunday too). He’s been told when he turns 10 later this year that he’ll be expected to do three, which will get him to where my wife and I are. But we’ve eased him up over the last few years.
We’ve tried to emphasize the responsibility that comes with things. Having things like toys to play with or a house to live in means taking care of them by cleaning them up. Being part of a family means helping each other out. Etc.