I agree with the posters here that pointed out that the way your hire your helpers might be the problem. My advise would be:
1. Instead of using an agency, rely on friends and/ or colleagues to get a helper recommended.
2. Always contact the former employer(s) for a recommendation, do not rely just on a recommendation letter that might be fake.
We hired our helper after the was recommended by a colleague of Mr. Elle, she has been working for us since 2001.
We don't treat het as a family member, we treat like we would like to be treated by an employer.
I genuinely believe many people have to swift through fdh because:
1. The fdh goes through a learning phase for the first month or two. New family, new country, new culture. Just when they learn of your routines and quirks, BAM your patience runs dry and she gets fired.
2. People expect too much.
The OP really reminds me of the traditional learning system in HK where they expect people to do everything perfect and have zero empathy for others.
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My experience has been that the more you communicate with the helper, the happier you will be. She can't read your mind. If you want things done on a daily basis or certain things weekly, you need to say so. As for cooking, you will need to teach her what you like and how you want it prepared. She may be a good cook in her regional cuisine or whatever her previous employer liked but may not know many dishes that you like. As others have suggested, there is a learning curve as each of you gets used to each other and the routines.
Sometimes when I get frustrated at some little thing she did/didn't do, I remind myself of all the time I am saving because she does so much.
Good luck with your situation.
Our helper's cooking skills are so bad we keep here away from the kitchen. That's okay as we never hired a chef.
For the OP: if you can't even manage to hire an FDH without such a carry on, I worry about you.