I think it’s easier than many of you think : keep Song Jiaoren (died March 29, 1913) and Liao Zhongkai (died August 20, 1925) alive. Their deaths were instrumental respectively to Yong Shikai’s rise to power and to Chiang Kai-Shek’s dominance in KMT.
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https://en.wikipedia.org/wiki/Song_Jiaoren
Fearing Yuan Shikai, Song Jiaoren quickly tried to control the parliament and mobilized the old Tongmenghui at the core with the merger of a number of new small parties to form a new political party called the Kuomintang on 25 August 1912 at Huguang Guild Hall Beijing. The 1912-1913 National Assembly election was considered a huge success for the KMT winning 269 of the 596 seats in the lower house and 123 of the 274 senate seats.
When the results of the 1913 elections indicated a clear victory for the KMT, it appeared that Song would be in a position to exercise a dominant role in selecting the prime minister and cabinet, and the party could have proceeded to push for the election of a future president in a proper parliamentary setting. After his murder, the trail of evidence led to the secretary of the cabinet and the provisional premier of Yuan Shikai government, Zhao Bingjun.
When the assembly convened for the first time on April 8 amid heated debate over the assassination, the Nationalists were divided over solutions on how to deal with Yuan Shikai, the provisional president who was suspected of the crime. Sun Yat-sen led a faction to rebel against Yuan on July 12 which called the Second Revolution but was completely defeated within two months.
The National Assembly members were compromised by threats and bribes from Yuan. He confined them and forced them to elect him formal president in the October presidential election. Next, he outlawed the Nationalists and expelled them from the assembly. Without a quorum, it could not convene so Yuan disbanded it on 10 January 1914.
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https://en.wikipedia.org/wiki/Liao_Zhongkai
Liao Zhongkai was the principal architect of the first KMT–CCP United Front in the 1920s. When Sun Yat-sen died in Beijing in March, 1925, and Liao was one of the three most powerful figures in the Kuomintang Executive Committee, the other two were Wang Jingwei and Hu Hanmin. Suspicion for his murder fell upon Hu Hanmin, who was then arrested. This left only Wang Jingwei and the rising Chiang Kai-shek as rivals for control of the Kuomintang.
Unfortunately most of my sources aren’t in English. Those quotes are from Wikipedia, but I strongly advice to read more about them. I do think that the butterflies induced by Song Jiaoren’s survival could help Liao Zhongkai to survive ITTL.
ITTL
In OTL, Song Jiaoren was shot through the window of the train by a man with a revolver. ITTL, the murderer decided to enter the train, but was quickly submitted by "eight fingers general" Huang Xing who travelled with Song Jiaoren aboard the train.
When the assembly convened for the first time on April 8 1913, amid heated debate over the assassination attempt on the President of the KMT. A military advisor to Yuan Shikai was implicated in the plot by Jiangsu authorities and newspapers linked Yuan Shikai with the murder. It was a rude awakening for many revolutionaries and for other party leaders. Conflict between Yuan Shikai and parliament intensified.
Before this attempt, Song was widely regarded as a prime candidate for the position of prime minister and when the new parliament opened, Yuan Shikai did not attend, fearing assassination. Nationalists exercised a dominant role in selecting the new prime minister and Song Jiaoren was elected in this position on the first day thanks of the support of members of the Republican, Unity and Democratic Party.
One of Song's main political goals was to ensure that the powers and independence of China's elected assemblies be properly protected from the influence of the office of the president. His party proceeds to push for the election of a new president in a proper parliamentary setting, calling for a temporary eviction of Yuan Shikai during the inquiry.
Three days later, Yuan Shikai pledges a formal complaint to the National Assembly and began mobilizing his loyal officers. On April 22, the general surrounded the building with armed troops besieging the elected representatives. The crisis has catapulted China into a new and unpredictable phase.
Most Revolutionary armies from different provinces were disbanded after the establishment of the Republic of China, and many officers and soldiers felt that they were not compensated for toppling the Qing Dynasty. These factors gave rise to much discontent against the new government among the military. Secondly, many revolutionaries felt that Yuan Shikai and Li Yuanhong were undeserving of the posts of presidency and vice presidency, because they acquired the posts through political maneuvering rather than participation in the revolutionary movement.
His government was in desperate need of money if he was to have a showdown against his enemies. He was supposed to he receive a 25 million pounds sterling loan from a consortium of foreign banks guided by their home governments – Britain, France, Russia, Germany and Japan – for the purpose of repaying debts owed the foreign powers (OTL Reorganisation loan). This agreement was found without approval from the parliament, a fact that was quickly revealed to the public by KMT newspapers.
During those events, Jiangsu authorities obtained a large amount of evidence which pointed to two of Yuan Shikai’s trusted followers. They were Zhao Bingfun who served as premier of the parliament and Hong Shuzu as secretary of the cabinet. Public opinion was incensed and anti-Yuan voices rose from all sides. Some in regard of Song assassination attempt called for the resignations of Yuan Shikai and Zhao Bingfun ; others with regard to the loans, demanded that Zhao Bingfun and Zhou Xuexi (the then Director of finances) to be impeached.
On April 25, demonstrators carrying Tongmenghui flags thronged outside the parliament building and in major cities. Foreign concessions were soon besieged by angry protestors. This new situation didn’t please Yuan Shikai’s foreign loaners, especially Japan and Great Britain.
On the same day, refusing Sun Yat-Sen’s advice of launching a Second Revolution, Song Jiaoren took a fateful decision, sending Liao Zhongkai and Huang Xing to the Japanese Ambassador, Ijūn Hikokichi.
... to be continued...
