Yeah, no that would not fly for a second. However, one note about the dirty house thing - is it starting off clean and she's making a mess and leaving it or is it, no offense meant, sort of messy to begin with and she's not doing any extra cleaning? Having made a living as a nanny I know that it would really irk me when a family had contracted me as a nanny and expected me to clean their house (for no extra pay) on top of whatever mess the kids made. cleaning any thing the kids did or dishes I/they used during the day was one thing but other than that not happening.
But that's really beside the point all the rest of that would be WAY more than I would ever put up with.
One other thing, whether you keep this girl (why you would I don't know) or hire someone else you should really have an official contract with your nanny that outlines exactly, point by point, what you expect from them in child care, cleaning, hours, sick-day protocol, what they are paid and when and what constitutes breach of contract. It protects you from them not doing their job and if they have any brain at all they'll know that it protects them from getting ripped off (not that I think you would but there are some pretty unscrupulous people out there). It's just a sugestion, I know it made things a whole lot easier for me.
....and no you're not crazy. ^_~