From my read, TM, no, it's not okay...especially considering the feelings you're having. (And we share a similar "having people leave" story). You made it particularly plain when you said it will make a two-week period without support and that's not good for ME. Excellent point to hang on to. That's the crux of recovery.
fwiw - of course, given the limited info I have - the second time I probably would have said, no, I will not reschedule. Granted, it's all-or-nothing and, yes, an ultimatum. In my book two back-to-back cancellations are unacceptable. Sounds like the T's actions, not words, have given you a good indication of how important you aren't.
I may be jumping the gun - hope the other guys weigh in - but sorry to say it sounds like it may be time to go shopping again.