Gosh your post really hit a nerve.
I went through the same struggle with my own Type 1.
Feeling overwhelmed with responsibility, denying I am any different than anyone else, denying that I have to permanently manage a condition to be normal, denying that my own body would fail me, feeling helpless that even the "best" I could do would still involve invasive and frustrating treatments.
For me, it was a phase. Happened at about the same age (through my teens, basically) and took about that amount of time to just get through it. At some point I learned that with a bit of management, I can thrive and do just as well as anyone, especially with the new tools that we have now. It just took that psychological struggle to get there.
I am really sorry that you have to see your daughter struggling like that. I know exactly how helpless it feels.