Oh wow... just wanted to chime in that this would bug me too. There's no way I could focus, or feel like I have T's full attention, if he had one of his kids waiting the entire hour just outside. No way! Definitely not appropriate... so sorry that your T put you through that!
Have you read about the concept of the "therapeutic frame". As I understand it, it's the "space" of therapy - and making that space feel safe enough for us to be open about our stuff. "Leaks" in the frame are when the outside world can intrude upon our therapy space... and these things can make therapy feel really unsafe, and create problems for us in opening up. This, to me, is a big leak. Though, if you want to commiserate at all, last week my T was in a new office... the office had an actual door leading to the outside world, with lots of windows. The next client actually WALKED IN THE DOOR in the middle of my session. *cry*. Luckily, this is T's satellite office - I'm usually not very loud, but I was very clear that I'm NOT coming back to this office. Oh heck, no, I don't need that at all - his normal office has no windows, and just the normal inside door - so it feels like a cave, which is ok by me!