Hello shanreagh and thank you for your explanation and taking time to help.
I had wondered if John and Mary's firstborn daughter Bridget was named after Mary's mother, but then I thought about just how common an Irish name Bridget is anyway. You may however be correct, and it could be a lead at least.
Thank you.
Here is the birth order of John and Mary's children all born in york:
Bridget Donnagan
1849–1889
Maria Dunnigan
1851–1883
Ann Dunigan ..my g. g. grandmother. She married Joseph Henry Holdstock.
1854–1931
Catherine Dunnigan
1858–1860
Catherine (Kate) Dunnigan
1860–1898
John Donnigan
1866–1927
===========
I began copying and pasting Mary Gaughan baptisms I found in Ireland from 1832-1834 and there are 11 so I stopped after the three below. The first one however may be a contender so far since she was born in Sligo and there is one of Mary and Johns son-in-laws living in York being born in SLIGO.
1) Name Mary Gaughan
Baptism Age 0
Event Type Baptism
Birth Date 2 Jun 1833
Baptism Date 3 Jun 1833
Baptism Place Kilmoremoy, Mayo and Sligo, Ireland
Parish Variants Ballina, Killmore Moy, Kilmore Moy
Diocese Killala
Father
Patt Gaughan
Mother
Bridget Mullen
Name Mary Gaughan
Baptism Date 14 Mar 1833
Baptism Place Backs, Mayo, Ireland
Father
John Gaughan
Mother
Brigt Newcome.
----------------------------------
Name Mary Gaughan
Baptism Age 0
Event Type Baptism
Birth Date 5 Mar 1833
Baptism Date 10 Mar 1833
Baptism Place Crossmolina, Mayo, Ireland
Diocese Killala
Father
Henry Gaughan
Mother
Catharine Hurt.
---------------------------------
Name Mary Gaughan
Baptism Age 0
Event Type Baptism
Birth Date 12 Oct 1834
Baptism Date 26 Oct 1834
Baptism Place Kilfian, Mayo, Ireland
Diocese Killala
Father
John Gaughan
Mother
Bridget Heraghty.
==================
Also two John Dunnigan , Dunigan baptism possibilities especially the one born also in Sligo...
Ireland, Catholic Parish Registers, 1655-1915
Birth, Marriage, & Death
Name: John Dunegan
Baptism Age: 0
Event Type: Baptism
Birth Date: 1831
Baptism Date: 5 Dec 1831
Baptism Place: Moynalty, Meath, Ireland
Diocese: Meath
Father: John Dunegan
Mother: Margt Brady
---------------------------
Name John Dunnigan
Baptism Age 0
Event Type Baptism
Birth Date 1831
Baptism Date 12 Nov 1831
Baptism Place Killenummery, Sligo and Leitrim, Ireland
Parish Variants Killenummery and Killery, Killerny, Killery
Diocese Ardagh
Father
James Dunnigan
Mother
Anne Lain