The Yun family's old folks' intentions, Lin Tian could certainly see through clearly. The Yun family is just like an ancient imperial family, where princes openly and secretly struggle for the throne, and as their father, the Emperor naturally knows about their contests.
But the Emperor doesn't stop them; instead, he lets the struggle happen because he knows that only this way can reveal which prince is outstanding enough to inherit the throne.
The Emperor wants his empire to last for centuries, and the heir cannot be a mediocre prince. In history, Li Shiming killed Crown Prince Li Jiancheng and forcibly seized the throne, which was a result of such struggles.