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I located a number of records which may be helpful. The first is Ellen's marriage record to Martin Morley. I did not find the marriage record involving Anthony Mulligan. The second link is the civil marriage record with Patrick Burke. I then located the death records for Catherine and Thomas Brett. I located the 1927 death record for Ellen Burke so Katie was 15 when she died. I searched for a Patrick Burke death record but did not see a good lead.
I then found the 1870 marriage record for Thomas Brett and Catherine Moran. Thomas' father was Patrick which is what you suspected. Finally, I located the 1871 birth record for Ellen Brett. I searched on the subscription site Roots Ireland and did not find any records for siblings of Ellen.
I may be able to contact someone who might have more information about your family.
Let me know if you have any questions.