Hello ezpz
You should have a read of the Employees Ordinance legislation which can be found on the Labour dept website
Read More.
Long Service payment is only due after five years. If you dismiss her now because of redundancy she will be entitled to severance pay, however if you dismiss her because of her poor work/misconduct you will not have to pay.
If I were you I would ring the Labour Dept to ask them based on your own specific situation, then you will have a clear answer as to what your liabilities are.
I would be worried having someone with no sense of hygene looking after my baby if I was at work!