I understand your black and white thinking in light of your experience with your last T! It's hard to find a middle ground! I didn't want to become dependent on my current T, not after going through it so many times before. But it happened anyway. I keep trying to find the middle ground but for me, maybe there isn't any.
If it's a pattern for you to become dependent, then it's something to work on with your T. It won't help to totally block her out so you can't get hurt again. We have to learn that relationships in RL aren't forever, either, and we can get hurt, but we need to connect with others anyway.
Since your T is former T's supervisor, so you say she must know about your situation with former T, I would suggest bringing it up with her. I know you don't want to do that, but then your reasons for pulling back now, from this T, would be out in the open and you can discuss them. I would ask her directly why she wants you to attach so much. Perhaps she wants to "do it right" this time, to undo the mess you got into with your last T? Saying she missed you sounds a bit much, but she must have her reasons. Instead of ruminating about it all, talking about it directly, as difficult as that may be, may be productive for you, in my opinion, of course.

