No, you are not unreasonable at all. We form a special relationship with our Ts, and it's perfectly understandable to not want to share your T with your sister.

I remember a former BPD friend of mine asking for my Ts information, because she wanted to make an appt. - and I wouldn't give it to her. I told my T about it, and he said he would refuse to see her. He said that there are plenty of other therapists out there, she doesn't need to see him.