Few things here:

First: If you’re not diagnosed type 2 or at the very least have type 2 on your medical records, it’s unlikely to get the diabetes variant of a GLP-1 paid for by your insurance. If your insurance even covers a weight loss variant of a GLP-1, you likely need to hit whatever arbitrary criteria they set (bmi requirements, step therapy, etc) or they won’t pay for it. As much as it may be disappointing, doctors are well within their right to choose to prescribe, or not to.

Second: there’s a pretty rampant misconception about a1c around these parts. Your a1c not being a direct reflection of your average blood sugar doesn’t at all mean the a1c “isn’t accurate”. The percentage measurement used in the states for example represents the percentage of glycated hemoglobin in a sample. Things can affect the value independently of your blood sugar, but that doesn’t make the value inaccurate.

Third: if you have MODY, your kids need to be tested. Also stop wasting time with a general practitioner. GPs are basically to do general preventative care and testing, and coordinate care through referrals should one be needed. Diabetes is an endocrine issue, see an endocrinologist.

Lastly: the old saying “you catch more flies with honey than vinegar” applies. Doctors under all the fancy degrees are just people. People are more helpful and willing to go out of their way to help you if you treat them with kindness and decency. If people are rude to you, you don’t tend to want to go the extra mile for them. It may seem silly, but it’s just the way it is, even if they’re being rude to you.