I don't think your T handled that too well. If she was in that much of a rush she could have called you back and arranged another time to talk. But getting snippy and then refusing to reassure you when that made you even more uncomfortable in what was already a difficult situation for you just cries out there was a lack of attunement.
As far as sometimes feeling warmth and understanding and sometimes cold and detached, I've definitely been through that with my T and most of the time I was projecting. But his response when I asked him if he was angry, tired of me, fed up etc. was to very warmly reassure me that he wasn't feeling that way. Not to make me feel like I being horrible to have those feelings. We have talked alot about how really strong emotions can feel like they must reflect reality but they don't always do so. That part of what happens developmentally with a secure attachment is that you learn to distinguish between reality and your feelings and ascertain how well your feelings line up with what's real. So I asked him how you figure out what's real when you lack the discernment and he told me you have to ask. He may have regretted saying that as I asked alot.

As for what you asked Shrinklady, I remember saying to my T once after he canceled an appointment that part of me wondered if he did it just to see how I reacted (I was pretty pissed at the time)? His answer was strong, clear and emphatic. He said there had not been, nor would there ever be, a strategic canceling of an appointment. That therapy is a reflection of real life and if you wait long enough, every situation comes up on its own, there's no need to create them. So I don't think she's playing games. She just may not have a good enough understanding of how you're feeling.
Bottom line (at last, she sighs!

AG