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This would bother me too. For me, it's important to know my T is "there" for me, and that I'm the most important thing he has going on during my scheduled therapy time. I think it would make me feel really small and unimportant if my appointment was constantly being shifted around because other people needed him more at that time.
I hope you will talk to your T about this. It sounds like a really tough spot to be in - to like your T so much, but to have to put up with being rescheduled all the time.
I wonder if there is a time when she is usually in town? I know I have a friend who travels a lot, but she is almost always in town on Friday evenings. Is there a time like that in her schedule when you could have a standing appointment??