When all the DCs were at home I did it this way:
I did all the laundry for me and DCs. This was the result of exH's strategic incompetence with fabric and water temps/ tendency to use bleach on colored clothes. He was welcome to ruin his own clothes.
All bedrooms had a laundry basket. Three baskets, five kids.
Each adult had one basket.
Bathroom had a basket for towels, and bedding went into that too.
Laundry was emptied into the washer until it was full.
Washer started, cold or lukewarm cycle run.
Everything was washed either cold or lukewarm. If a second load was needed, that went on after thr first came out.
All bedding and towels were white and went into a hot wash along with whatever else needed a hot wash (kitchen towels, etc).
Dryer filled, clothes needing hanging hung.
As soon as the dryer was finished, clothes were taken out into the baskets, folded, sorted into piles, and put away. Hanging clothes were sorted and folded and put away as soon as dry too.
There was a dedicated time for laundry operations - usually Saturday afternoon and the task was done from start to finish at that time.
You have too many cooks spoiling the broth here. One person should be doing the laundry or if more than one person does it, there shouldn't be confusion about what's clean and what's not.
Do all your washing at the same low temp and you won't have laundry sitting around waiting for the right temp wash and careless 'helpers' bugging dirty items on top of clean stuff.