Being too harsh over a double booking?

I booked my first lesson in where my test is going to be. I couldn’t get any in London but there were loads in my hometown. Everyone from my best friend (who passed here) to my regular instructor said it was the best move as it would be easier and I know the roads better.

So I booked a lesson about 3 weeks ago when I knew I was coming back. I paid her two days ago and she confirmed payment. I came to where she asked to meet but couldn’t see her. Called her to which she responded “who’s this?”.

I then told her and she was like “omg, I didn’t put you in my diary” and I’m just in disbelief at this point. She then puts the suggestion of telling her current lesson that she would have to re-book but I’m like that’s not fair. She’s about to get into your car. You cannot reschedule there and then. Also, if you did that with her, you could absolutely do that with me at some stage. She also offered to meet me after this girl but I already made plans as I only have a few days to see my friends.

She then asked what I wanted to do and I just asked for a refund. I’m not sure if I should have been more lenient but I was so annoyed as I couldn’t believe she had done this after I literally confirmed payment 2 days prior. She’s also more expensive than my usual instructor (which I find shocking), so that stung even more