It’s not just about speaking the language, it’s about the qualification and the academic structure, not to mention the cultural element which my child will always lack not living in the country.
Has it occurred to you that perhaps this is as it should be? For whatever reason, this is the country you now find yourselves in and for your DD it will be 'home'. To raise and educate her as if she were living elsewhere seems quite cruel to me, unless the goal is to move (?back) there at some point during her childhood. But from what you say about this school taking her til 18, that seems not to be the case. Depending on her temperament, I can see that she might end up feeling like she doesn't belong anywhere - not here, but not other-country either, not in her home neighbourhood but not in the one she commutes to either - and also if the goal is to immerse her completely in another country's educational structure, curriculum and exam qualifications, I suspect many of the other pupils will be there temporarily while parents work abroad (here), so there'll be a lot of churn in her friendship group. It seems like her actual needs are being sidelined to indulge someone else's (your mum's?) fixation on the superiority of the 'old country'.
When I had a discussion with my mum about her going somewhere else she said over her dead body would we move her elsewhere.
This is all kinds of wrong. And it sounds like your insistence on the thread that you won't move her is actually your mother speaking. You yourself seem to be quite open to the logic of it - unsurprisingly, as all this effort and stress must be leaving you in a lot of physical pain if you have MS.
I think you need to unpack some of the complex emotions and motivations in this picture, as without that you're doing both yourself and your DD a massive disservice, all so that your mother shouldn't have to be upset about anything.