How many times do I have to say it!?

I help teach an 'after school' class with a teacher from a hagwon. Until recently, she taught 1 class on Monday afternoon and we shared a class on Thursday afternoon. No longer. Without any notice, she changed the schedule to accommodate some personal tasks. How did I find out? Why, I turned up to class and the door was locked, of course! This wasn't a problem since the classroom is next door to my office but I was a bit miffed that she hadn't bothered to call or email to tell me things had changed.

Now she's trying to wrangle me into teaching this class at some strange times. The conversation so far has gone like this (and I'm paraphrasing here):

CT:  Can you teach in the mornings during term.
Me:  No, I teach regular classes in the mornings.
CT:  Can you change it?
Me:  Um, no. It's set by the school. I can teach in the afternoon.
CT:  OK, can you come in before 8am and teach then?
Me:  No. I don't start work until 8:30. I can teach in the afternoon.
CT:  OK. Can you teach during the holidays?
Me:  Sure, as long as it doesn't interfere with the 2 camps I'm doing. Then I gave her the dates/times I'm teaching.
CT:  You're busy when I want to teach in the mornings. Can you come in before 8am in the holidays?
Me:  No. I don't start work until 8:30. I can teach in the afternoon.
CT:  It's not convenient for me. Can you teach Saturdays?
Me:  No.
CT:  You're not teaching that week. Can you teach in the mornings then?
Me:  No, I'm on holiday in Seoul then.
CT:  Can you change it?
Me:  No

Yeah, I'm a little irritated. I understand she has some personal things to take care of and that it involves trips to the hospital. But this is country where people go to the hospital for a sniffle and she's assured me she's OK. Nevertheless, I'm prepared to negotiate and teach when I can during working hours, when I'm free to accommodate her (my schedule is set by my school, after all).

Having said that, I don't think it's unreasonable to be consulted before changing a schedule I'm expected to follow (how can I follow it if I don't know what it is?). What I do think is unreasonable is for someone to get cranky when I don't accommodate them by not wanting to teach at the crack of dawn or on weekends.