Well I guess it's just a different viewpoint. In my family education is expected until 21. There was no option to drop out at 16, would never have crossed my mind or that of my cousins. That doesn't mean that I think that children should get no choices, I chose my O levels and my A levels, and the school I went to at sixth form too. I jut wouldn't have been given an option that involved me living alone at that age.
I think you are missing the point. DS1 has an MSc - but it was his choice. DS2 lived by himself while doing his A levels - and again it was his choice. Nowhere did I suggest dropping out at 16 - and nowadays it wouldn't be legal anyway. DS2 wanted to do A levels - in a particular choice of subjects. He did not want to do the IB. We accommodated his choices.
Of course we all have aspirations for our children - but what is best for them isn't necessary concordant with our ambitions. Sometimes you have to let them make the decisions.
And as for not being given an option - a parent doesn't have that level of control over a 16-year-old. But you make it sound as if I'm advocating young people living on their own from 16 - of course I'm not. The majority of them do and will continue to live with their parents while they do their A levels or whatever, and they will be perfectly happy. My point was that sometimes circumstances dictate a different approach, and if parents work with it rather than throwing up their hands in horror then a successful conclusion can be reached.
So to get back to the OPs original question - should her daughter be left alone while parents go on holiday - yes, of course. For the following reasons:
That's what she wants to do. (Had she wanted to go away with them, that would be fine too.)
At 16, she should be completely capable of looking after herself.
She wants to work - that's very laudable, especially considering the number of threads about lazy teens.
She cannot be forced to go against her will, despite what the "insist" brigade may think. So she may vote with her feet, as one PP actually did.
I must admit, the comments about her saying "I hate you" do suggest a lack of maturity, but consider this:
If she really is a bit immature, a couple of weeks fending for herself might make her grow up a bit.
But I suspect the tantrum is really her venting her utter frustration that her mum is refusing to even consider what is a perfectly reasonable - and fairly normal - request.