I'm learning about the Mexican revolution and I'm a bit confused on what the Constitutionalists, Zapata, and Villa stood for. What did each group seek to reform and how did they plan to achieve it? Why didn't they work together?
The trick is to not think of the Mexican Revolution as a coordinated revolution, but rather a civil war.
The Zapatistas, Constitutionalists, and the Villistas (Division del Norte) all had different constitutencies, different goals, and different strategies.
The Constitutionalists focused on the issue of political reform through a new constitution. Madero and later Carranza saw political reform as the mechanism to achieve broader social and economic change. They supported armed revolution to depose the Porfirio Diaz and then Huerta. But after that they believed that constitutional reform would suffice.
Zapata did not necessarily believe that simple constitutional reform would suffice. He supported the Constitutionalists to bring down Diaz and Huerta, but his faction wanted greater structural and institutional change in the constitutional discussions. They would split from the uneasy alliance during the constitutional convention that would eventually produce the Constitution of 1917.
Villa represented an interesting figure. Villa was very much a populist who did not have as clear or consistent vision of a post revolutionary state. He tended towards opportunism in forging his political alliances.
The take away should be that the underlying problems of Mexico ca. 1910 were severe and there were many different views about how to enact social, political, and economic reform. Between 1910-1914, a coalition defeated the long time dictator Diaz and his erstwhile successor Huerta, but that alliance could not hold because they did not agree on a vision for a post revolutionary Mexico.
In the end, the major post-revolutionary party PRM/PRI grew out of this uncertaintly by building a broad coalition that included agrarian interests (the Zapatistas' base), business interests (the constitutionalists base), and laborers.
The big success of the PRI was to begin to create a national memory of a 'revolutionary family' in which Zapata, Villa, Madero, Carranza, etc. could all be heroes of the nation even when they spent most of their time fighting each other.