In order to search in Sligo, you really need more information.
1851 2283/192/18
Abbey Road Knaresborough
Bridget Molrooney head widow 42 yrs Farm servant b Sligo
Michael Molrooney son 16 yrs farm servant b Sligo
Thomas Molrooney son 12 yrs farm servant b Sligo
1861 3204/ 109/10
Grotto, Knaresborough
Bridget Malroney widow 63 yrs Laundress
Michael Malroney son 24 yrs Mason's labourer
Thos Malroney son 22 yrs Bleacher
James Firth grandson 5 yrs b Keitley Yorkshire
James was born Keighley I think in 1871 and there is a birth for James Mulrooney in 1856- don't know where 'Firth' comes from.
Bridget and sons are born 'Irland'.
As you can see Bridget's age varies but this is quite common.
1871, Bridget is at Spittalcrofts, Knaresborough aged 65 yrs.
Is Mary's marriage in 1853- Edward Milner and Mary Moran?
It would be best to check her father's name from her marriage certificate.
regards
heywood