I hope your problems with injecting at school are now over, as your daughter is probably up and running.
I read all the posts on here, and feel compelled to contribute from the viewpoint of having type 1 for over 30 years from the age of 13, seeing the children with diabetes at primary school, the ones at our high school (where I work), and working with the person who implements the Health Care Plans.
Firstly, primary school children will need help with looking after their diabetes at school. And from what I have seen they get it. However, my neighbour still needed to bring her daughter home for lunch everyday to ensure she actually ate. But that has resolved itself, and that is what DLA is for, to cover not working or reducing your hours.
Secondly, unless very newly diagnosed, a 12 year will be expected to inject herself (unless she has a disability that prevents that). We were inpatients back in the day, and made to do our injections from the very second dose. Secondary school WILL NOT normally receive any extra funding for diabetic students. But will make provision for them. Extra funding is normally only available for severely disabled children who require an assistant with them. A diabetic doesn't.
The Health Care requirements doesn't specify that secondary school students must have someone in to do their injections. I wouldn't want to be held responsible for giving insulin to a teenager who subsequently decides not to eat their lunch. We hold any medical supplies the students need and extra hypo treatments. I have even stocked the cupboard with spare meters and strips, just in case. We have policies that they can test and eat in class. I have even held CPD sessions for staff on how to understand their diabetic students and all the things they have to cope with all day.
Teenagers do not want to be different from their friends, and there could be nothing worse than having to go off to Mrs X to have their injection, and being "special".
I hope your daughter is finding coping easier now with a little experience under her belt. It will get easier, and I wish her the very best. By the summer she will be a pro and able to cope independently.