Well, someone paying a high price for peace of mind is one thing, yet this helper is blatantly refusing to do the things that her employer has requested she do; she ignores the children and stays in her own room using her computer and phone for hours when she should be looking after them (kids can get up to all sorts of things when not being supervised!); she denies them food and refuses to provide them with the food that the employer would like ... to me, this would not offer 'peace of mind', and I personally wouldn't call it 'being well cared for'!
Also (as well as all the other issues that the employer has with this helper), because her previous employer was out on Saturdays, she doesn't expect to have to cook or do anything for her current employer on that day. She even has the cheek to tell her employer 'no' when she asks her to cook a certain dish! And, whilst it's a fairly trivial matter with regards to the Wellcome stamps, if the employer wants to keep them for herself, that's her right ... how dare the helper assume that she has a right to them just because her previous employer gave them to her?! I give my stamps to my helper because I'm happy to do so, but in the beginning had she so much as hinted that she thought she should have them, they would have gone straight in bin!!
This helper is way too troublesome and is dictating all the terms to her employer. If the employer wishes to keep her for 'peace of mind', then that's up to her, but if she was happy to do that, then there's no point in complaining about all the other issues that she's obviously not happy with.
The OP said, "Appreciate your comments and how to address this in a constructive manner."
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I assume when you interviewed her you outlined what you expected her to do, such as cooking for the family, etc? That being the case, she has no reason to refuse you.
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Absolutely not! As long as you outlined what you wanted her to do when you employed her, you are only expecting her to do what is in her job description ... many employers expect far more from their helpers, sounds to me like she got an easy life and you're pussy footing around her to make it even easier!
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Expecting her to look after you kids, feed them what you would like them to be fed, and expecting her to cook for you the dishes that you would like, and do the clearing up afterwards, is not too demanding ... it's only what the majority of helpers do everyday without question ... because it's their job ... it's what they get paid to do!
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You ARE being 'taken for a ride', and the longer you let it go on the worse it will become. You need to sit down and have a serious discussion with her. Every family is different, and has different wants and needs, make sure you tell her this! She can not expect to do everything the same as she did with her previous employer ... YOU tell HER what you want her to do and how to do it, not the other way around! And if she's not willing to listen to you and take on board what you ask her, then you have a choice to make ... it's up to you ...