I suspect Mary was actually Irish Catholic (based on daughters marriage), daughter of Thomas Malley and Maria Murphy of Dublin.
Name: Maria Malley [Mary Malley] Baptism Age: 0 Event Type: Baptism Birth Date: 1809 Baptism Date: 19 Mar 1809 Baptism Place: St Nicholas' (Without), Dublin city, Dublin, Ireland Parish Variants: Francis St., St. Nicholas (without), Francis Street Diocese: Dublin Father: Thoma Malley Mother: Maria Murphy
She died at the age of 38 on April 9th, 1848 in Liverpool. She was buried on April 11th, 1848 in Liverpool.
Death Notes
Died before 1851
Name: Mary Woodward Gender: Female Marital Status: Married Age: 38 Birth Date: 1810 Death Date: 9 Apr 1848 Burial Date: 11 Apr 1848 Burial Place: Liverpool, Lancaster, England Spouse: John FHL Film Number: 1595423 Reference ID: it 7 #6485
General Notes
In 1841 John (35, a labourer) and Mary (30) were with their children Ellen (10), Daniel (8), John (6) and James (1) at St. John's Village, Islington, Liverpool.
James was born on May 4th, 1840 in Toxteth Park and his baptism took place on May 17th, 1840 in Liverpool.34
Birth Notes
Aged 1 in 1841
WOODWARD, JAMES MALLEY GRO Reference: 1840 J Quarter in LIVERPOOL Volume 20 Page 379
Name: James Woodward Birth Date: 4 May 1840 Baptism Date: 17 May 1840 Parish: Liverpool, Lancashire, England Father: John Woodward Mother: Mary Woodward Register Type: Bishop's Transcripts Reference Number: Drl/2/157