I hope that if you let this cool a bit, she will realise she was unfair. I think there is a lot of 'sensitivity' going about, as we see from posts on this forum.
I think that your GP's decision was sensible and one I would have taken.
It seems to me that there is a disconnect between the vaccinations organised at GP surgeries - where the staff have local knowledge from car parking to bus routes to household organisation; and those organised at large centres where they can only use the data provided, and have no idea how folk will get there, how able they are to stand in a queue etc.
Our lovely surgery in a rural area is now vaccinating just-turned-70s. A family friend in her 90s in another area was just offered 2 places to get vaccinated - both large hubs in cities and both over an hour's drive from her home. She is waiting for someone to get back to her about somewhere nearer. I should add that she lives in a densely populated urban area, and I have no idea why the local surgeries are not vaccinating.
How do you acknowledge Easter.