Ann Fadiman details the struggle in The Spirit Catches and You Fall Down between the Hmong and American culture. Did history and the challenges the Hmong tribe faced affect their culture?

The Spirit Catches You and You Fall Down depicts the difficulties faced by the Lees--a Hmong family from Houaysouy, Laos--whose second youngest daughter, Lia Lee, suffers from Lennox-Gastaut Syndrome. The book deals with the trouble that cultural traditions and lifestyle cause for Lia's medical treatment while examining the more universal experience of the Hmong people and the discrimination they have faced.
Thus, to answer your question, yes, the history and challenges the Hmong people have faced have most certainly affected their culture. The rise of communism in Vietnam after World War II and increasing Chinese oppression caused the Hmong people to migrate from northern Vietnam, southern China, and Thailand into Laos. Unfortunately, the Laotian government was overthrown in 1975 by Communists, resulting in the deaths of one-third of the population of Hmong living in Laos. Another third migrated to Thailand and then elsewhere from there. A small number of Hmong immigrated to the United States.
Additionally, many of the Hmong remaining in Laos were forced into re-education camps under the reign of the new Laotian government of the Lao People's Democratic Republic in the 1970s. The end of the Vietnam War--which Hmong soldiers had participated in in order to aid the CIA--had drastic consequences for the Hmong. They faced genocide and forced migration; even those who managed to escape to Thailand were forced into concentration camps. The Hmong faced the sense that the American forces had used them and then abandoned them to poverty, disease, hardship, and death. 
Some Hmong immigrated to the United States in the mid-1970s; however, assimilation proved to be quite difficult due to the culture clash. Some customs familiar to their homeland--such as the marriage of girls at the beginning of puberty--created legal trouble in the States and resulted in the prosecution of Hmong men for sexual abuse. Polygamy, courtship practices, and early motherhood faced equal Western scrutiny. In order to survive, the Hmong were forced to Americanize themselves and reject parts of their culture that were once critical. This was also done through practices of intermarriage and the abandoning of the Hmong language. Consequently, life as the Hmong people used to know it has all but disappeared.