I’ve had T1 a long time, I can’t give you advice regarding convincing or hard selling something to your daughter, but I have a pump, and a CGM, I was previously on shots for 29 years, and I have had a1c’s way up the 12’s and in the low 6’s.
My opinion on CGM is they are great tools but the technology isn’t there yet for me. There’s the battery, there’s the transmitter, then there’s the warm-up and the calibrations, and the re-calibrations, and then there’s the warning on every cgm on the market: “Device is NOT a substitute for finger stick tests” and the false alarms, and the lost sensors, the weak signals… etc. The point is that the current CGM technology is not the end-all of modern instrumentation. I use mine for basal rate adjustments and for trending when I feel like it.
In my opinion, very satisfactory results can be achieved with 8+ finger sticks a day and aggressive insulin therapy including (if she’s not on a pump) mealtime and correction bolus shots. Based on my pump feedback, I’d be averaging 8 shots a day. I’d average way more shots and testing than that if I snacked.
I know your daughter must seem very young to you, but you may seem unyielding to her, so this could be a very sensitive issue. Maybe one thing you could do is to talk about just what is an acceptable a1c. maybe her goals are not too different from yours in that area, and maybe there’s a way of achieving common a1c goals in a manner that is acceptable to both of you. The ADA suggests that “good control” is at or below 7%, I have a personal preference for below 6.5%
I can feel your frustration; you don’t want your daughter to have complications and her current level of control is making you nervous. It’s still emotionally and physically a different perspective for those of us dealing with an incurable disease every day. I think working together would be better than being adversaries. As she grows, she will ultimately be 100% in charge of her health anyway.