Patricia, where did you get the name Edward "Byrne" from?
The extracted record from the IGI has his name as BYNE on the bapt for Harriett (illegitimate). Was Byrne recorded somewhere else?
What date and where was Margaret's marriage? Who did she marry?
As her name was Ellison she might have thought it easier to put her mother's dead (or disappeared) husband/partner for father's name, especially if she didn't know her father.
The two girls were aged 7 in the 1851 census as you know, mother a widow with older children. The bapt date in the extracted record for Harriett was 15 NOV 1844 Saint Barnabas, Douglas, father Edward Byne, mother Anne ELLISSON.
The Source is given as Saint Barnabas, Douglas 1849 - 1867 LDS film number 0106186. Note the dates - if it is on this film, and the film really starts in 1849, it was recorded years after the given date.
The IGI also has "This information was generated from another entry that appears in this index. Look for another entry for this person".
The other entry, presumably, was her marriage to JOHN KELLY on 6 OCT 1867, Braddan. The Source for this entry is LDS film no.0106189. [Braddan parish register.]
You need to look at BOTH these films, to see whether Harriett's record of baptism includes her twin sister.
The films can be ordered to view worldwide for a small fee at any Family History Centre, or at the MM. See the phone book for the closest FHC, under Church of Jesus Christ of Latter-Day Saints.