I don't think you are unreasonable at all, and I'm glad to hear that the agency seems to have the situation in hand. I discussed a slightly similar situation with my T, except in my case I was trying to get T to agree to see one of my closest friends who was also looking for a T - but my T will not under any circumstances do therapy with two people who know each other well, and he explained why, and it made sense. I think many Ts would reason like that, and am sure that if an existing client asks them not to take on a family member, they would have every reason to take that request very seriously. It's about your feeling safe in your T's office.