Sorry that happened to you. She sounds very flaky, not to mention totally incompetent.
I used to think my pdoc was bad since he's habitually 20 minutes late, but wow, that lady is much worse than him. Personally, I would not tolerate someone who is that late. I'm already having a hard time accepting 20 minutes.
You should not have to deal with the b_llshit of "well, I'll have to talk to the head psychiatrist first..."
Honestly, that is NOT fair to you. You are paying for an appointment because you want to accomplish a simple medication change. You should NOT have to pay for two appointments to accomplish what you want. That is criminal.