(1) To make its narrative intelligible, the show necessarily simplifies many events and characters. Tang Shaoyi is one such example. An ivy league graduate and experienced politician, I do not think Tang would have been so curt and uncordial with foreign ambassadors or with Yuan Shikai.
On the surface, Tang was the ideal choice for premier, as the most favorable towards Sun Wen’s party among Yuan’s familiars. His early resignation is a defeat for the hope of a joint government.
(2) Simplification also leads to the discrediting of Lu Zhengxiang. Lu is by any account a skilled diplomat, who would later do his best to represent the Republic of China at the ultimately unsuccessful (from the Chinese standpoint) Treaty of Versailles. This is why he is not remembered very fondly in public perception (though I doubt anyone could have done better in Versailles), and may be why the show portrays him as incompetent in this short stint as premier.
It must be said the true reason for the failure of the second cabinet, much like the first, is the fundamental divide between Yuan Shikai and the United League. No qualities of individual cabinet members could have changed that.
Lu Zhengxiang also has a fascinating personal character. A devout Catholic, he retired from politics to live out the rest of his life as a Benedictine monk in Belgium, eventually being named the abbot of the Abbey of St. Peter in Ghent.
Chinese Shows Translated 