I once ended things with a T after an episode a lot like what you're describing. It was the last of many instances of inappropriate behavior and crap boundaries on her part though, not the first issue with an otherwise great therapist. I think it's almost unforgivable to have you meet a member of T's family when you're going to your session. Especially because in this case, since the daughter is a teenager, she could have waited for her mother at a nearby coffee shop or something.

I feel crappy when my T cannot give me an extra session especially when I'm in crisis. However, when you consider the compromises a T might have to make to accomodate you and the impact these might have on their focus (for eg because they're rushing, have children in the waiting room, hungry on their lunch hour, crazy overtired) it might seem more worthwhile to find another way to cope until your nest regular session.