Hi John,
Who did Mary Ann/e marry please and have you obtained her marriage certificate as this should give her father's name and occupation?
Posting the info below to assist others in the search

1881 Pentre Row
RG11/ 5516/19/31
John Edwards wid 70 clerk
Edward " 19 coalminer
John "15 "
Mary Ann " 18 housekeeperLouisa Eliz. " 10 sch
John " grandson 1 b.Broughton
Unless stated born Brymbo.
1871 Mount Pleasant Inn, Cerney
RG10/5656/12/17
John Edwards H mar 60 publican
Margaret " wife 33
Margaret " daur 11
Edward " son 9
Mary Anne " daur 7John " son 3
Louisa Elizth " daur 7mths
All born Wrexham
Is this John in 1861 living ? Gyfnnes, Brymbo.
RG9/4277/42/1
John Edwards H unm 50 farm 50acres b.Brymbo
Mary Sweeney unm 30 dairymaid b.Ireland
Hugh Hughes unm 40 labourer b.DEN
Mary Jones serv 21 b.Brymbo
Margaret Jones daur 1 b.Brymbo

This would appear to show Margaret to be the child of John and Mary

Do you know the family's religion? There were lots of non conformist chapels in the area and the baptism registers may not have survived.
Have you tried contacting Wrexham Register Office to see if they can help locate the correct birth?
http://www.wrexham.gov.uk/english/life_events/bereavement/register_office.htm