In Act II of Nixon in China, the Nixons attend an opera, The Red Detachment of Women, and find themselves involved in the action to a degree beyond what they had expected. Though the opera-within-an-opera is the creation of John Adams, Alice Goodman, and their choreographers, The Red Detachment of Women is a real-life work. Based on a novel and film of the same name (which were based on historical events), it exists in both ballet and operatic versions, and was the occasion for the meeting of the Nixons and Mao Tse-tung's wife, Jiang Qing.
In her book Nixon in China: The Week that Changed the World, Margaret MacMillan describes the performance and its reception (page 275):
". . . Interpreters whispered the plot in the Americans' ears but it was not difficult to follow, because the good characters—peasants, Communists, guerrillas—bounded on looking noble and upright while the villains—landlords and their minions—slunk on with averted faces. In spite of the propaganda, Nixon found it an enjoyable spectacle. 'This is certainly the equal of any ballet that I have seen, in terms of production,' he told American reporters. 'It was,' thought Haldeman who had also enjoyed the performance, 'rather an odd sight to see the [President] clapping at the end for this kind of thing, which would have been horrifying at home, but it all seems to fit together somehow, here.'"
A complete film version of The Red Detachment of Women (ballet) is available online through archive.org. The official video description describes it in glowing terms and suggests an underlying feminist message: "It depicts a woman's journey into the People's Liberation Army. Instead of weak, fragile women dressed in fluttery tutus, women were depicted in military uniforms with rifles. Instead of frail motions, women had strong arms and clenched fists. This play shook the entire foundation of bourgeois art."
John Adams, in his notes to Nixon in China, is much less flattering in his re-interpretation of the work:
"The second act ballet, The Red Detachment of Women, a study in agitprop dance, theater and music, was based on a political ballet from the period of the Cultural Revolution that had been shaped and ideologically massaged by Madame Mao. Mark Morris’s choreograpy featured the same absurd images of ballet dancers on point, dressed in the uniforms of the People’s Revolutionary Army and brandishing rifles. In composing for this scene I set for myself the equally absurd goal of making it sound as if it were the creation of a committee of composers, none of whom were sure of what the other was doing. This followed the line of the tradition of creating 'people’s' art."
According to its Wikipedia entry, it remains a favourite with Chinese audiences, and is a permanent part of the repertoire of the National Ballet of China.