Your T made a massive mistake by giving you so much information about what is going on and by allowing you to take care of her. This never should have become an issue in your therapy. She sounds so close to being a good, thoughtful T, but this life stress appears to be compromising her judgment. I think anything that happens in therapy is fair game for you to respond to, so she shouldn't bring in anything about herself or her life that she hasn't dealt with sufficiently to be able to handle whatever response you had. She should have said, "I am dealing with a family health crisis. I am fine, but it is going to affect my availability in the following specific ways. Now, how are things going with [therapy thing you have been working on]?"

I said something to my T once about a situation that wasn't nearly this life-or-death, but it was very critical of her and was completely not my business. (Something akin to me saying she was a bad parent because of a parenting decision she made.) She responded by validating my feelings and working through it without snapping back at me or getting defensive. She has told me since then that even when I was being critical of her, she could hold onto who she knew herself to be and not be overly influenced by my strong feelings. And dissecting my feelings and why I responded so strongly was hugely helpful for me. It would have been a missed opportunity if she had gotten defensive in the way your T did.

It is also jaw-droppingly unprofessional for her to speculate about whether she was moving. Do that with your friends or in your own therapy, lady! I have had similar issues with being afraid my T will move away, and when I expressed my anxiety, she said, "I understand why you're worried, and I will tell you that I have no plans to move right now." Boom. If she did decide to move, I know that she would only tell me if she was 100% sure, and she would think about the best way to tell me and what I would need during the termination phase. She wouldn't let me drift around in her free-floating anxiety with her.

Your T is right about this being a boundary issue, though. Specifically, it's about her inability to hold good boundaries. You did nothing wrong. The client gets to say whatever the client wants to say. Her inability to see this even after she has cooled down means that she needs to take some time away to deal with her personal life and emotions rather than dragging them into the room and making them your problem. I hope she can work this out with you, but I think your feelings about this situation are justified. Therapy needs to be about you and your needs and your issues. What she is doing around this rupture is not therapy.