For your son, you should change the maid. You do not want your son to learn behave like her, right?
She does not respect you as the employer and she does not treasure the contract. She will not put BB and your work in priority.
You must give the maid warning letter if you want to fire her without paying one month's salary in lieu of notice. It is time to keep a close eye on your maid as there is someone not trustworthy in your home taking care of your baby.
you can tell your bun bun that according to the contact, she cannot stay overnight (as she came back home at 1:00am). And you need to tell her that as she lost her ID in Hong kong she need to report to the police (which is under the HK Laws). Let see what does she say??
it is better to issue warning letters, point out their faults. If they will not improve, then you are in a position to fire them.
Otherwise, if your bun bun appeal to immigation or labour that you unreasonably dismissed them, then there is a case for you to respond.
They have a right to do so. So better serve them warning letters and send a copy to the agent as your witness. If the bun bun is not employed thro' agent, then get a third party to witness your serving a warning letter to her. Trouble trouble but you better do it proper to save problems in future.