I believe you just found another ancestor of mine that I can now add to my tree...Maria Unferdorben.
My great grandfather was Istvan (Stephen) Unferdorben, born 22 Feb 1873 in Balinka, and married first Carolina Wagner (also from Fejer county) 6 Feb 1897 in Passaic; prob at St Mary's Assumption RC Slovak church and had 3 children - 1 son that lived only a few months and 2 daughters: Carolina who was called Lena and went into the convent and died young (abt 22 yrs old) and Agnes, who later married George Grisgraber and after a short time in Passaic they move to Southbury, CT. Carolina Wagner's parents were Anton Wagner and Eva Peidl and Carolina died abt 1902 in Passaic from TB.
Istvan then married Wilhelmina Marinisz [AFTER ONLY ^WEEKS!] (church records spell it Morenecs) in Passaic and then moved to Southbury, CT. and had a son Alfred that only lived a few months, then Martin, Helen, Florence and Mildred. Istvan died in Southbury in 1914.
Istvan had a sister, Anna (also from Balinka, born 19 Aug 1875) and she married George John Grisgraber of Istemer in Fejer county). Istvan and Anna's parents were Istvan Unferdorben, born Aug 1849 in Balinka and Katlin Stohl or Szoht, born abt 1855 in Balinka.
I believe that Istvan, Sr's parents were: Jakab Unferdorben and Teresia Schweighardt.
From familysearch.org I found that Jakab and Teresia had an Anna Maria born 11 Jun 1841 in Balinka and a Katalina born 7 Jan 1844. Katalina apparently married a Jozsef Schveighart, born abt 1840 (I thought also from Balinka) and they had a son, Kristof born 20 Sep 1844.
Maybe you and I can compare trees and see how these families fit together, as they certainly seem to be related.
BTW, what was your trip to Hungary like? I intend to travel there next year. I have the name of a genealogist from Istemer that is also a Grisgraber and likely related and she also speaks English.
I hit a brick wall, however, with Istvan, Jr's 2nd wife's family...my maternal greats as the girls'mother was widowed twice when they arrived and I have no idea of a maiden name. But I believe she was from Ungvar.
I have lots of pictures and genealogies of some of the families if you are interested.