Bismarck and Fredrich III hated each other. Bismarck is gone the second Fredrich becomes Kaiser. Bismarck treated the Crown Prince with contempt there is no way that a health Fredrich will allow Bismarck anything. I suppose this was posted in "After 1900" because the effects will be felt after 1900?
Fredrich is 56 thus a find candidate if he is anything like his father for a long rule well into 1914 and beyond. He was rather liberal by Prussian standards and anti military, which may have caused some friction. I read something about him wanting to clarify the powers of the Chancellor and the Monarch. This may be interesting...