I don't necessarily think asking about the eating lunch thing would be inappropriate, though a bit weird. However, it would certainly bother me (and maybe it's also inappropriate) if a second T I was talking to talked about how they felt special to my actual T. I can see how it can seem like she's competing.

I agree with the others that you've never seemed to fond of her and that alone for me would be enough to not see her anymore. As far as I know, he's also her supervisor? I agree that that's also a weird triangle going on with which I can see many things that can go wrong. I'd usually say if you have two therapists, try for them to not be connected.

I'd suggest you still bring your service dog with you, maybe that calms you down a bit with her so you can stand your ground if necessary?