We have -
Catherine Lunergan
1893 LONERGAN Catherine mmn MOOR Audenshaw Tameside AUD/60/2
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Probable birth registration of William Moore son of William Moore & Catherine
1880 MOOR William mmn CONROY Audenshaw Tameside AUD/43/57
Catherine Conroy/William Moore marriage 1862
Catherine Moores/George Chappells marriage 1885
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I think the only way is to possibly get 2/3 certificates

1893 Catherine's birth.
Then if it matches, 1889 marriage of Michael Lonergan & Mary Ann Moore 1889
Then maybe William Moores & Catherine Conroy 1862.
It does look as though the family connection between Catherine Chappells & Catherine Lonergan is on the Moor/e/s side.