Can you set up a rota op?
I'd bag everything per person then
Monday night put in bath towels for the four adults. Hang out early Tuesday morning. Fold as they come off the line.
Tues after school run put in a load of toddler clothes. Hang on airers. If it's stained or doesn't fit, bin it before washing.
Tuesday teatime do a load of yours and onto the airers. Move before bed or in the morning.
Tuesday night put in a load of towels for the kids plus hand towels etc. Hang out early Wednesday morning. Fold as it comes off the line.
Wednesday after school run, put in a load of the school kids clothes. If it doesn't fit etc and you aren't keeping for the toddlers, bin it.
Wednesday tea time adult 2 does a load of theirs and onto the airers. They move it before bed or before work.
Wednesday night do a load of bedding - focus on bottom sheets and pillow cases as a priority. Put out Thursday morning.
Thursday after school run, do a load of anything left over of the kids
Thursday tea time, adult 3s turn.
Thursday night do a load of bedding. Put put Friday morning.
Friday after school run do anything left over of the kids.
Friday tea time is adult 4s turn.
It comes off the airer / line and is folded and put into rooms. If you're dressing the kids fro ma pile of clean clothes, fine.
Saturday is uniform day and putting away.
Sunday is a whatever is left day and putting away.
Everyone has a washing basket / bag for life in their room. Washing per person or types of people makes folding and sorting easier. It comes down on the day it needs washing.
Tows hung up to dry so can be reused. Either change out of uniform and rewear both for a second day or leave it on until bedtime.
Adults take responsibility for their own clothes on the day specified. If they need to do a second wash typically it fits around your plan.