As someone who can also read into a 'perceived' tone in texts and emails I don't see anything wrong with her first email response. Perhaps it is a tiny bit business like in it's use of direct language but seems genuine and clear. She was trying to accomodate you by saying she was willing to come into work earlier to see you which not all therapists would do. The piece about the mandatory meetings also gives a reason as to why she isn't available which is fair.

Did you tell her you would like the 7am time slot if there were no cancellations? If not she may not think that appealed to you therefore not said it again when there was no cancellation. If it is something you want I would ask her if you can still do that.

Also, as someone else said if you don't ask. your questions you won't get any answers.... she won't know what you are thinking/wondering so it will all be left unsaid/unanswered.