Daoism, Confucianism and Legalism represent the three great classical philosophies of Chinese history. Interestingly, they all have their origins in the period following the disintegration of centralized authority under the Zhou Dynasty. All three philosophical traditions do contain a political dynamic. They contain very different answers to the same question: how is political stability best achieved?
For Legalism, the answer lies in rule of law and, if necessary, oppression. Legalists shared a deeply cynical vision of human nature, which informed their punitive vision of law and order, which they believed would instill respect among the populace for said law and order. This vision was critical in influencing the Qin Dynasty, which unified China under the first emperor, but it also contributed to that Dynasty's quick demise.
Meanwhile, Confucianism was founded from a moralistic picture of society. Ultimately, according to Confucian thought, society is founded in relationships, which, by their very nature, entail mutual duties and obligations. Confucianism envisioned a deeply hierarchical picture of society and of human interaction. For the most part, Confucianism imagines human relationships as unequal by nature. For example, it understands human interaction as based within one of five key relationships: that between the ruler and the subject, father and son, husband and wife, older and younger brother, and that between friends. Of these relationships, only the bond between friends is viewed as fundamentally equal: in all other cases, a hierarchical relationship is envisioned, with one held as superior over the other. However, in all cases, each party owes certain obligations and duties to the other. The key to establishing a working and harmonious society, then, is for the people within that society to recognize the obligations and duties that they owe to one another and to honor them.
Finally, Daoism is in many ways the most difficult to understand, given that its teachings are deeply paradoxical. In many respects, it is opposed to the kind of systemic thinking built into Confucianism and Legalism. Instead, it revolves around the Tao, the abstract way. The Tao is both reflected within nature and transcends it, and likewise transcends easy understanding. Thus, the Tao Teh Ching's first chapter closes with the statement: "The Mystery of mysteries is the Door of all essence." (Tao Teh Ching, Transl. John C. H. Wu, Shambhala: Boston, 1990).
Daoism contains a radical anti-authoritarianism which opposes both Legalism and Confucianism. Consider, for example, the words that open Chapter 17 of the Tao Teh Ching:
The highest type of ruler is one of whose existence the people are barely aware.
Or Chapter 30, which begins:
He who knows how to guide a ruler in the path of Tao
Does not try to override the world with force of arms.
It is in the nature of a military weapon to turn against its wielder.
In these sections of the Tao Teh Ching, one sees a rejection against the focus on hierarchy and authority which Confucianism and Legalism share, advocating for a system by which political power, whenever possible, ought not to be asserted, viewing such shows of force as self-destructive and self-defeating.