The OP does not seem to be asking the cleaning lady to do degrading stuff. Being asked NOT to clean up the playroom so the kids do it on their own is not degrading. Nor is folding laundry. (I love folding laundry so my cleaner doesn't get to do it)
So all this is kind of irrelevent.
I think it would be very easy to find a cleaning lady who would be happy to do/not do these things. So yes, I would fire this woman.
