As an addition to the information that Mark gave you, Rudolf's immigration in 1902 can be found under the spelling Hadovszky. He indicates he was from K. Hnilec (K = Kis = Little).
Agnesa indicates her mother was Cecile Pachmaja from "Hinilac" and she was going to her brother-in-law Martin Pachmaja in Pittsburgh. Martin Pachmajer immigrated in 1898 from Delava, just south of Hnilec.
Microfilms are available from your Family History Center for the Roman Catholic records for Hnilec. However, I have researched another village not far from there and found that many of the early records were actually German Lutherans. Hnilec is also found under the names Nagy (Big) Hnilec and Nyilas. The records for that village also include those for Delava.
The records for Kis Hnilec are on line.
Between the two sets of records, you ought to be able to research both sides of your family.