Hello,
you could try to get a birth certificate for baby Margaret - the best I can see in Free BMD is a Margaret Carlin though

A birth certificate would give father's name and mother's maiden name.
There is a marriage but it is 1862 for a Patrick Celleahen and one female spouse is missing in the index but there is nothing to say that it is a possibility.
You would imagine that there would be other children had the marriage been that early.
There is also a Catharine Cahelin birth 1867 and a Catherine Calahin death 1868 -aged 0yrs.
There are several Cahalan variations in the Yorkshire area (not Bradford though)
Where do you have Bridget or Margaret after 1871?
There is a marriage for a Bridget Cahillan 1874 -the only spouse being Bernard Henry but I can't see them in 1881. If that is her, the marriage certificate would have her father's name.
That's odd though as Bridget and Margaret are in 1881

heywood