Hi Rebecca,
Welcome to the forum.
I have 2 daughters who are Type 1, the oldest is 14. I am sorry your parents are so unable or unwilling to help you with your diabetes. You sound like you are doing a great job, your HbA1c is fantastic, well done! And in such a short time, it's amazing!
I don't have much advice about how you can get your parents to be more supportive, quite honestly I find their attitude pretty incomprehensible. Anyway, I wanted to say something about your early morning ketones. If your blood glucose is okay, that almost certainly means that you are having sufficient insulin. If you are having sufficient insulin, then your ketones are almost certainly so-called 'starvation' ketones, produced because you have not eaten all night. Non-diabetics often produce these ketones too, especially children and young people. Ketones become dangerous only if you have too little 'background' insulin, and this is when diabetic ketoacidosis can develop.
If you are still worried, please ask your consultant about it. In the meantime, keep up the good work, keep your chin up and good luck with your parents. Please keep posting and let us know how you get on.
Sue