What events brought Mao to the decision to rely on the PLA to restore social order? What were the conditions in Chinese society like by this point?

Mao's decision to use the People's Liberation Army (PLA) to restore social order emerged in the context of the Cultural Revolution. It involved his inability to control aspects of that social transformation. Particularly problematic were the Red Guards, a kind of paramilitary youth movement that initially had Mao's support. The problem of the Red Guards was somewhat analogous to that of student movements and radicalism in the West, like the Students for a Democratic Society (SDS) in the U.S. It was, however, far more serious and violent.
The Red Guards first served Mao's purposes, helping him destroy the last vestiges of a pre-Communist China. They were involved in significant actions to destroy symbols of an older China. But as the Cultural Revolution progressed (one might say "devolved") the Red Guards became increasingly violent and uncontrollable.
Their mass movement tactics of murder and humiliation (which led to many suicides) eventually became unsustainable, and when Red Guards got out of hand in 1967, students were told to desist and return to "normal" and go back to school. When it proved impossible to control them Mao decided to turn the PLA loose. This resulted in brutal military reprisals and the dissolution of the Red Guards throughout 1968.