If you like this T, I'd definitely call and explain the dilemma. Perhaps T does have the flexibility with advance notice. You have nothing to lose by asking. Also, perhaps you can schedule regular meetings and in the event sister is unavailable you can have your session over the phone. I have done phone sessions when sitter canceled last minute, or if I was expecting the exterminator at that time; it worked for us.
Best of luck on working this out.