Hmmm.
Sorry, I think this is about what role you play.
She can't have it both ways, and neither can you.
You are still acting like 'Mum' to two full adults. Actually I think it is a major invasion of privacy to be going in and getting their washing, or going in their room at all. So what, if it piles up behind their door?
You picked up your DS's jacket, if your own free will, and put it in the wash with his shirt. Your choice: you took a responsibility there. I'm not saying your Dd isn't behaving badly, she is. But stop your Mum role, and tell her to behave like an adult.
Stop the ironing, not in a vengeful, punitive way, but just to re-balance the whole set up.
Treat people like toddlers and they will behave like toddlers.