Alison,
This looks like it could be Deborah's marriage, found on the IGI:
Batch M040144 / Film 0378770
William HUGHES & Deborah PETTEY marr 26 Jan 1834, Saint Thomas, Dudley, Worcester, England.
Oldbury is only 3 or 4 miles from Dudley. No other PETTY marriages in that batch, which goes way back into 1700s.
Father's name is probably not given on the original document - if it were, it would usually be recorded in the IGI entry (fathers' names are given for marriage after civil registration started in 1837; also before then for under age marriage where father's consent was needed).
However if you view the film of the original document at your local LDS family history centre, there will be at least 2 witnesses to the marriage - you may just get lucky with those names.
Mary's death certificate would probably show her husband's name (under the field for occupation!) eg. "Widow of

Petty". However this is not guaranteed - UK death certificates are not very informative in my experience.
Cheers,
Steve