I think that family dinners are incredible important. That sitting and talking about the day matters. I would not be jumping up to start washing up etc while family are sitting and eating.
Please don't give in to those saying cut dinner short.
The thing that stands out from your post compared to when my kids were little is that you are home at 4, but don't eat until after 7, and don't finish until after 8. I assumed when I first saw your post that you were arriving home at 6.
That (late meal) and that alone is what means you have no evening.
When I was home at 4, and dh home at 6:30, dinner was on the table ready to eat at 6:30, and lunches/dishwasher/laundry etc has been done.
If your dh is the main cook, then he cooks at the weekend, and makes one/two meals in advance for during the week. It is unrealistic to arrive home at 6:30 and start cooking with young children.
OR you do everything the other way round. Assuming you are eating at 7, then before dinner, in that slot from 5-7 when kids are playing etc, you empty dishwasher (make this 8 year olds job?), clear away dry washing up, prep lunches, fold laundry etc.
So the only thing to do after dinner is pack dishwasher (10 minutes max) which could easily be 12 year olds job, and then do the washing up.
You cleaned the house in that slot today, but that doesn't need doing every day, so most days you can crack on with this stuff.
Also a bit of multi tasking - make lunches while doing dinner. Unpack dishwasher while kids are eating breakfast, put away last nights washing up while kids eat after school snakc etc.