Hi insanity:
I wonder given this could be autism (or potentially aspergers) if the solution may lie in explaining the logic of knowing about these things. Certainly with asperbergs you can be battling the 'why do I have to know this stuff/ why do I have to hear about things that upset me/ etc...' and they can be very resistant to hearing that it's considered part of the course/ everyone has to do it/ it's a hurdle you have to jump too.
I may have this wrong - but have you considered with ....
Cells - most 'cell work' is with plant cells in Y7 (e.g. DD1 made a thin section of onion, placed it on a slide and stained it red, put on the cover slip and looked at it in 3 different magnifications under a dissecting microscope). Now given pretty well every meal at home involves slicing onions - she was in no way distressed by this activity.
She was clear that this was teaching her about plant structure but obviously related to structure of any living organisms, although cell structures varies in animals from plants.
Most of this is presented in cartoon form in school books - so isn't overly graphic. It does explain how your body works (collections of cells form tissues and tissues form organs (skin, heart, longs, etc...) and it also helps to explain how life evolved from single celled microscopic forms.
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History - was she as disturbed in primary when she was learning about the Greeks, Romans or Vikings? Terrible things have happened in the past but the point in learning history (hackneyed though this is) is to help us avoid the mistakes of the past. Knowing terrible things happened (e.g. millions of deaths in World War I) and appreciating the disaster of that for families, friends, ordinary communities - whatever side of the war - is an important lesson.
Again - I think it unlikely in Year 7 they're showing piled up bodies from Auschwitz/ former Yugoslavia/ Rwanda - but these things have happened. Understanding how they came about - the mistakes that were made - what could have been done to stop such tragedies is important.
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I'm not sure what the English content was - and again it is upsetting when someone dies in a book. I sobbed like a baby every time in Charlotte's Web - worse since I became a mother actually. But feeling that affection for a character, sympathising with their plight, feeling angry/ upset/ afraid for them is what makes literature so important - it isn't just a nice story - it sometimes is a social commentary or makes a political point by affecting us in such a way.
For example - I found To Kill a Mockingbird a tough read at 13, it does involve rape and murder - but the humanity of Atticus Finch and the bravery he showed in the face of an angry crowd - standing up for the rights of Tom or Boo and portraying some really unpleasant aspects of the American south from the point of view of children (Jem, Scout & Dill). It says volumes about what is right and wrong about American society and gets you thinking about the person you want to be.
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I totally sympathise that rationalising like this with your DC might not be an easy or straightforward process - but perhaps if she can see past the upset of the subject to why it might be necessary to know these things - how it could help her develop as a person/ be useful to society - may just help her to better cope and potentially avoid that desire for 'flight' in the face of a situation she finds distressing/ upsetting.
HTH