The name of the father of Moses and Aaron still alludes me. However, today (4 December 2015) I have discovered a few entries in the JewisgGen that might throw some light on this subject. There is a record of the documents of US and UK consulars in Jerusalem, Jaffa and Haifa which were turned over by the Americans to the Israelis sometime ago. There are three entries there that are of interest. A document (UD #408 Haifa, Vol 14, page 11) relating to Philippos Hornstein in Jaffa dated 11/5/1866. Another one (UD #453 Jerusalem Vol 125 page 4 doc. number 20) to Isiah Hornstein dated 1867. He is described as a Rabbi. And finally, document (UD #448 Jaffa, Vol 24, p 225) relating to Joseph Hornstein. There is no date. We don't know what these documents relate to. There is an entry for Moses Hornstein of Kolel Romania dated 19 Apr 1916 in Jerusalem. It could be regarding our Moses but the date is a bit late as our Moses died in 1885.
From a sworn statement we have, obtained from the Prussian Archives dated 6 June 1855, we know that their father had converted to Christianity "four years ago" (c. 1851) was both a resident of Safed and Jerusalem. Something has been lost in the German translation as it is not clear reading the English version whether or not their father is stilll living. In a desperate attempt to retain German protection, in a petition to the Chancellor of the Reich, Prince of Bismarck, however he mentions that his father died shortly after his conversion to Christianity in 1851.
There is also an entry dated 11/04/1915 for Mr C Hornstein (which I believe to be Charles) and A Hornstein dated 1/17/1882, of Germany, which I believe is likely to be Aaron.
From all these entries Joseph Hornstein seems to be the most likely candidate although he seems to be from Jaffa. There are no dates of the entry so without access to the record it is impossile to say.