YANBU OP.
Nobody has the right to tell you they are staying the night in your home.
There is a thing on here where you cannon mention family providing childcare without some posters insisting this means you give up any right to complain about anything they may do and that you've basically signed over your life to them to dictate whatever they want in return.
That's not true.
My PILs did this to BIL and SIL. They found a fantastic nursery for their younger boy, then MIL had a massive tantrum about wanting to care for him herself and how she's never been good enough for them and they'd rather pay good money to strangers than let her have a relationship with her grandson.
So BIL insisted they give up the nursery place and let PILs have their son instead .
And then MIL used to ring up the rest of us complaining that she had to give up her hobbies and couldn't just get in the car and drive to visit her family whenever she wanted to because she was babysitting all the time. And if SIL did anything that MIL didn't like she would start with the "So we're good enough to look after your child but not good enough for…"
And they did things like you have mentioned, gone through private cupboards, opened post, snooped, pushed boundaries, expected their own way over everything because "we're doing you a favour", lots of things like that.
What you have said here OP has reminded me of that.
YANBU. Staying overnight on a Monday provide the childcare she insisted on being allowed to provide on Tuesdays does not give her the right to tell you she's spending other nights in your house as well.
It doesn't. It's your house and your home. She doesn't get to tell you that she's staying in it.
I'd let your DH tell her that, with as much as a little tact as he cares to use.
One thing I have learned from dealing with my PILs (who we are no-contact with now because of their behaviour and who managed to drive BIL and SIL to emigrate in the end) is that while you are trying to tiptoe around them using tact, they are trampling all over you with no tact whatsoever.
Which is what is happening here, telling you she is staying in your house.
You don't have to put up with it just because she provides a favour that you didn't want and didn't ask for and which doesn't suit you because she often lets you down.
So I'll say it again, YANBU at all to say no to an uninvited guest telling you they are going to spend the night in your home.