Surely it doesn't matter what the actual issue the OP has of the MIL doing her laundry is, she has asked the MIL not to do it, and she still does it, that is the problem.
I am assuming if you hire a babysitter you wouldn't want them snooping round your house.
I would never go into someone's bedroom unless they told me it was ok. My bedroom is my private space. And usually if we have guests staying it's usually where all the rubbish that currently resides in the spare room, has to be moved to, so I really don't want people seeing it.
Some people are just more private.
We have had other threads where MILs/DMs have come in to the house and rearranged cupboards/furniture. Again I would find that really intrusive, other people may be ok with that.
It just seems very odd that when you have asked someone not to do something, they keep on doing it, when they do not actually need to do it. If you were expecting her to sleep in dirty bedlinen and you told her that you didn't want her washing it, then that would be different. Although in that case I would bring my own bedlinen or not stay over. But MIL does not need to wash your clothes, unless you have run out of clean clothes and are having to walk around in the nude, and if that was the case, that would be one huge dripfeed from the OP!