As a point of clarification, the books titled "Vinaya Texts" vols 1-3 was translated by T.W. Rhys Davids and Herman Oldenberg. [1881-5] and seems to contain the patimokkha(rules only no stories) and the Khandakas. The Khandakas do contain background stories, but not to the patimokkha rules. If you scroll down on this page you can find themhttp://www.sacred-texts.com/bud/index.htm
I believe a print on demand company called Forgotten Books will sell you a hard copy.
I. B. Horner translated both the Suttavibhangha and the Khandakas(Under the title Book of Discipline) , but I don't think they are in the public domain yet. My recollection is that there are several PTS scanned books on archive.org claiming to be the Book of Discipline but when you download them they are something else.
Ajahn Thanissaro's Buddhist Monastic Code will often have a summary of the origin stories, although not for every rule. Certainly enough to give you an idea.
Hope that is helpful(and correct