Sounds like her therapy approach is not at all what you are looking for. It seems a bit stilted and cold; wouldn't work me either. I doubt you will change that. You can either spend weeks and months analyzing why this isn't working for you, or you can accept it isn't working for you now and move on. It doesn't sound like these are things that you will be able to just overlook, drop, and continue with.
Personally, I've never had my therapy become more about the therapy relationship than me. That would be a red flag to me. I don't really believe that therapy HAS to be about the relationship at all and can be entirely effective without all the complication of that. I have had good working relationships with my therapists, but they were comfortable, fairly open, and always focused on what I needed to do to heal and move on. They never got bogged down in the therapy relationship. I know that for many people, the relationship is everything in therapy, but for me, that just seems like it would add more complication and misery to an already complicated me. I don't need the therapy relationship to bring on more problems for me; if it does, then somewhere we've lost the plot. Others here will definitely disagree with me on this. I only know what works for me. The fact is, YOU have to know what YOU need in YOUR therapy. Seek it out.