@James321 I'm not a parent, but I was a teenager with diabetes. I was 16 when I was diagnosed five years ago, and when I got to about 18 (so about two years in) I... rebelled. To put it mildly. Being asked what my blood sugars were made me really, really angry. I hesitate to call it an eating disorder, but I developed a very unhealthy relationship with food, where I would binge eat and not inject, then inject and not eat for days.
I'm on a better track now, and something that really helped me is getting a Freestyle Libre, which my grandmother very generously pays for. You can scan with a phone, and whilst it doesn't replace finger pricks, it's better than nothing if she isn't testing at all. At first the novelty of it had me scanning, and then because I could see what I was actually doing to myself, that encouraged me to start trying again. For some reason, the graph seems to have more meaning to it for me than the number on the metre.
As a parent I am sure you want to constantly ask about blood sugars to know how she is. I can't speak for her, but for me it just felt not only like my parents didn't trust me, but also it became a subject of immense anxiety every time my sugars weren't perfect, which sometimes they just aren't. SO maybe try to restrict yourself to asking once a day. Instead, why don't you try asking her how she is - show her that you are interested in her, not just the diabetes, or if there is anything that you can do for her. When I am really struggling, my boyfriend asks if he can make me a cup of tea. It reminds me that I am loved, and that even though it feels like it, there is a world beyond diabetes.
I know you've said she would be resistant to it, but I have found this forum to be a great support. Alternatively, does she do twitter? I don't, but I believe there are several rather good accounts of diabetics, and I'm sure the same is true of other social media sites. This is a very lonely disease, and I would guess that she feels that you don't understand. Which you don't. But that doesn't mean you don't care, or feel for her. Perhaps she doesn't want you to feel sorry for her. I'm not a psychologist, and I'm not in her head, I can only relate from my own experiences.
Sorry for the essay!