I am starting to get some clues here.
First of all, the "egg shaped" tumor...I've never heard a bladder tumor described this way....broccoli shaped, I've heard of...in trying to make sense of this, along with the clue that this famous Doctor wanted to take this case because of it's rarity, then there is something here that we are not familiar with...
Also, the Doctor says it's not Cancer, and obviously he isn't so concerned about getting it out...maybe there are people under his care who do have cancer and need the surgery room and surgery skills in a more timely manner than your sister does...
Or, maybe all of this is wrong and your Sister needs to go for a Second Opinion...but, where do you go for a second opinion when you are already at the top..
If the Doctor has told your sister to go home and to deal with her feelings the best that she can until it is her turn in the surgery, then he has said what he wants to say to her.
If she wants something faster, then she is going to have to take the bull by the horns and go someplace else...
Remind your sister that APPROACH and TIMING is everything. I know this from being a public servant. When one of the public comes at us with impatience and attitude looking for answers and help, then I have seen many time when myself or my co worker become less and less willing to give the help that they need....human nature, I think...
Telling you this with the best of intentions...
Rosemary