SPOILER Warning

Reposting my answer to questions about the power play between Xiao Wuyi, the Empress Dowager and Li Mao/Grand Tutor in Ep 4 palace coup:

Prince Jing'an and Xiao Wuyi have a 200k Beifu army - that is enough power to change dynasties. They can be kingmakers if they so choose or seize the throne themselves. Throughout Chinese history, powerful generals have ascended to the throne - Tang, Ming, Song etc were all great dynasties founded by generals.. The emperor needs them to keep the enemies at bay on the one hand and fears them on the other hand. He is sickly and vulnerable, his cousin Prince Changsha means to seize power. Although Prince Jing'an is a titular prince, he is a wàixìng wáng/外姓王 or prince with a different surname meaning he is not of the same bloodline as the ruling imperial family Li. They were probably enfeoffed as wang/prince in recognition of their contribution to the country - Prince Jing'an (his father) probably helped the founding emperor establish their dynasty.

Per the Grand Tutor, the ED is reckless and incompetent. She wants to eliminate any threat to her son's throne (and her power) at all costs. She doesn't care if the defective crossbows cost them 5 cities (which Wuyi took back) as long as it undermines Wuyi's military power. She also pinned it on Prince Changsha, killing two birds with one stone. Wuyi had no intent of rebelling until he discovered the ED's duplicity - he was not willing to step down or allow his men's lives to continue to be endangered by this reckless biatch. But the emperor gets the big picture and he stepped in to do the right thing - by installing Prince Qi as regent he checks the power of the ED and balances the power of the court. Of course at that point, Prince Qi cannot marry his maternal cousin Jiayu - that would make them too powerful an alliance and look like he gunning for the throne. He has also tied his fate to guaranteeing Wuyi's loyalty - if Wuyi rebels, Prince Qi is dead.

As for why Jiayu had to marry Wuyi - Jiayu's mother is a Princess with the ruling surname Li - she is either a cousin or the sister of the emperor. A marriage between Wuyi and Jiayu binds the Xiao family to the ruling Li family. It also allies the Xiao family with the Xie (Grand Tutor's) family. The power dynamics and setup of this story is all about balancing power and interests. That is the game the Grand Tutor is playing. And if Prince Qi is really his secret illegitimate son, then he is scheming to put his son on the throne. If the sickly emperor dies with no issue, it is clear that Prince Qi is well positioned to immediately assume power. He is most likely the mastermind behind everything. The ED is too stupid and near-sighted to plan so far and so deeply. In subsequent episodes, we see that the Grand Tutor knows his son Li Mao lacks ambition of his own. He also intends to use Jiayu's budding relationship with Xiao Wuyi to motivate his ambition - by making him fight for the girl, he forces him to try to be more powerful than Xiao Wuyi.