she hates being diabetic
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Sadly, I suspect this is your answer. She hates being diabetic. She hates being different from her mates. Different from 'everyone else'. Just...different.
As others are saying, if she is in denial, or rebellion, or whatever, I doubt any 'good advice' from either parents or 'experts' is going to make a difference.
What she might listen to, though, is her fellow teenage diabetics. Is there a forum for them, or whatever social media she's likely to use? Something that will engage her, and make her feel less 'weird' etc etc. Make her feel part of a 'new group?
I know it sounds nothing like, but as a newbie to this forum, I now feel a lot more 'at home' with my DX, and less 'weird' myself, so hopefully it can be similar for volatile teens?
Teenage girls have so often a totally toxic relationship to food anyway, even without the complication of something like diabetes, so it's going to be hard for her.
Also, if she's always had a junky/sugary diet (??) she (probably??) has never been sporty?? So can there be a way to turn her around completely (ie, almost outwith the DB), so that she develops a body-positive attitude, and wants to make the most of her appearance, not sabotage it with poor diet and no exercise? (It doesn't have to be sport - absolutely not - any exercise she likes, eg, dance, gym, whatever, will pay dividends)
(I make allowance that it could be that she is very sporty and so has got away with a junky/sugary diet!!!)
This may be a bit farfetched, but maybe (?) you (or, more like, her peers) could 'sell' DB to her as a mechanism for getting fitter, through good diet and sufficient exercise, all round (and therefore more attractive!) (OK, not trying to sound like appearance is all, but for a teenage female it's usually a VERY high 'want' on their personal agendas.)
Could you possibly set 'rewards' for her, I wonder? eg, if she sticks to a lower-carb, healthier diet, gets some kind of exercise regime going, then you'll reward her with something nice - an outfit she wants, a concert she wants to go to, whatever whatever? It could be the motivation she needs to help her turn thing around?
I do wish you all the best possible - teenagers, let alone teenage girls, let alone teenage girls with a health issue, is not easy............