Here’s Owen’s marriage in 1863. Note his wife gave her name as Mary (not Elizabeth). Owen’s address was Mullaglass (Mullaghglass) and the bride’s was Carrickneenan.
Elizabeth’s & John’s births in Mullaghglass:
Here’s Peter’s birth at which time they were living in Cloughreagh. (Mother’s forename Mary).
Griffiths Valuation for 1864 lists Owen Callaghan on plot 35ba in Mullaghglass – a house and small garden (typical for a labourer at that period).
Mullaghglass was in the RC parish of Killevy Upper. Their baptism records start in 1832 so Owen might just scrape in (and you might find details of any siblings born later). The RC parish records are on-line free on the National Library site:
Tracing back before 1832 will be pretty difficult due to the lack of records.
I looked for a likely death for John Callaghan but did not see one of the right age 1864 onwards (which is when death registration started). I suspect he died before that, in which case there will be no record unless he has a gravestone.
John Callaghan was a farmer according to the 1864 certificate. If so he should have been listed in the tithe applotment records. Those for 1834 & 1835 m list a John in Sefin (Seafin) townland. There were also several other Callaghans farming there too. So that might be him. There’s no John Callaghan listed there in Griffiths but there is an Elizabeth (usually when a woman was listed she was a widow). And she has the name John in brackets after her entry suggesting she was John’s widow. She had plot 42 & 43 which totaled just over 7 acres.
She died in 1882 aged 90:
Ages were just a guess in those times and could be out by 10 years or more. I can’t say that is definitely Owen’s mother just it’s the only one that I can find that fits. Seafin is very close to Mullaghglass so she was in the expected area.