I'm so sorry this happened to you with your T's next client- it's understandable to feel very upset. My appt with T is the last of the day, but another therapist and her client are supposed to begin their session in the same room at exactly the time we end ours- impossible, right, especially as my T is often running late. At 7pm on the dot I can hear the other T pacing outside (she even just opens the door sometimes)- I get so stressed I feel sick. I once heard her client tell my T off because we had overrun- it felt horrible...
Your situation sounds worse because this is also your T's client. I think your T should try to protect you by asking the client to remaining in the waiting area until she tells him it's his time, and by asking him to bring up any complaints he has only once he's in the room... may not work though...

It sounds like there are other things to talk to your T about (e.g. what she makes you call her vs. how other clients are allowed to address her) but perhaps the situation with the next client would be a good starting point and you could build up from there?