Your husband is correct, get rid of her, she is breaching the safety of you home and trust, and all this in the first 2 weeks of a contract!. Imagine what she might try to do if she is left alone while you are on vacation. These friends/relatives could have been dismissed for stealing-- you don't know! and she is letting them in your house. No matter whats she says is the reason for them being there, ie looking for work etc, it is still not allowed, they could be in HK illegally.
In fact if you read the rules I have attached she may even be eligible for instant dismissal
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I think the info is on pg 18 you will require,
If you need an FDH in future, only take one who comes preferably with very good references, from a last employer you can speak to, maybe someone who is leaving HK. Make a list of all the requirements you as a family need in a helper.
Make some rules, and make sure the next helper obeys them, helpers are there to help, not 'walk all over you',
I am sorry this has happened with your first employee, but it might be an idea, if you print off a set of HK Imm rules, so you know and have easy reference to what a helper can do, and cannot do. If they know you are a rookie employer, lots will take advantage, and bend the rules to suit themselves.
Good luck with the next one, who may be perfect.