Not the best arrangement to be sure. It sounds like she handled it in a competent way (but her initial lateness was unacceptable unless also related to this crisis call--someone on staff should have alerted you to the delay, if that were the case), but it is a poor policy on the agency's part. They should have someone available perhaps also serving in a walk-in basis covering emergency calls.

I'm sorry it upset you, and I think your reactions are totally understandable. You deserve--and your therapy deserves--a respected space.

The only times in 11 years that my hour was ever interrupted was once a phone call that T had to make before my session, he saw me and apologized for the delay before making the 10 minute call; and another time the bell on his outer office door rang during a session, and he excused himself to check it out because he wasn't expecting anyone. The first occasion was within an agency setting, the second in a private practice setting.