I think your T really screwed up. First she changed the session time, then she was late for it, then she left early. Clearly she was not available and should have been honest about that. It was wrong for her to take your (or your insurance's) money for that appointment because it was cut short and she did not give you her full attention.

Telling you her daughter would be there and you could meet her was all kinds of wrong. It implied that you wanted to meet her; it implied that you felt her daughter was important to YOU; it showed off how much she values her daughter when I believe you've said she knows you are a bit jealous of her daughter; she had to have known you would feel awkward having an hour long session knowing this girl was just outside the door waiting; you knew her focus and attention wouldn't be on you but would be on 'cherished daughter'.

LEAVING the room to go talk to her daughter was just unbelievable. I'm shocked at that one. Clearly she was thinking about her daughter and whatever the two of them had going on at that moment, and not you. It was blatantly unfair and terribly unprofessional and I would think rather invalidating for you.

I know you like her but her boundaries are really bad. And I know bad boundaries can feel wonderful to clients and clients feel special and loved and all, but in the end, unless the T is prepared to begin a real friendship once therapy stops, the client gets left high, dry, and very, very hurt. I feel like YOU are fulfilling some need SHE has, and that is causing her to get so very personal and friendly and blur these boundaries so badly, and that's not fair to you.

Personally, as much as you like her, it sounds like it's not the healthiest fit for you.