The real Dolours Price was married for two decades (1983-2003) to the Irish actor Stephen Rea. During that period, Rea appeared in the movie for which he is arguably best-known in the United States: the 1992 romantic thriller The Crying Game. In that film, Rea plays Fergus, an extremely reluctant and ambivalent member of the Irish Republican Army (IRA)--the same organization that Price was involved with for many years.
Dolours and Marian Price had three siblings, Clare, Sean and Dino but they are not featured or even mentioned in the series.
This is based on the book of the same name by Patrick Radden Keefe.
The name "Dolours" is derived from (and refers to) The Seven Dolors (or Sorrows) of the Virgin Mary in Roman Catholicism (although the Price family were not, especially, religious).