I also can not tolerate this kind of maid and I think I will fire her. Start to hire another maid privately and when the new maid arrive, you can dismiss her. The reason for dismissal is she keeps on disregarding your orders/regulations. This is only what I think, maybe you should talk to your agent. My own maid is also no good at all (but she's new and green) and I keep thinking if I should change her as well.
if your maid does not change after warning (verbal and written), better get a new one...
you girl will soon forget about her. don't worry too much. as long as your new maid is goodhearted and knows how to play with your girl, your kid should have no problem with the new one. it just takes a bit of time.
You must find a new one, even your daughter doesn't want to have. I really hate the maid who doesn't like to be controlled. It must waste my time to teach her.
For you as her employer, you must set up some clear rules to her, eg. wake up at 7am etc. If no rules, she will try to check your bottom-line. So you can't be so nice to them.
There are so many maids in HK, I don't believe that I can't find a better one to replace her job.