Maybe she doesn't know you've already seen a psychiatrist. Can you tell her that and offer to answer any questions about what that pdoc talked to you about?

Her behavior does sound strange to me. Do you think she might be afraid of her safety? I'm not trying to imply anything negative about you, just searching for a reason why a T might demand a pdoc visit before meeting with you again. I've never heard of that before. Could it be that she believes there is a chance that your issues are outside of her scope of practice and wants to know for sure, and thinks a pdoc could better make that determination?

Her inability to communicate clearly to you the reason behind her request is not a good sign in a therapist, IMO.