John and Mary Dunn were parents of my great great grandfather. Have only limited info on the Dillons:

Notes for JOHN DUNN and MARY HERTNAN DUNN:
Emigrated to the U.S. probably through Port of New York on or about 1852 with 4 children, and probably with Robert and Rosina Dillon.
(Oldest gravestone in St. Patrick's Cemetery is for Robert Dillon, died 1-17-1857, aged 35 years; his probable spouse, Rosina, continues to reside adjacent to James Dunn (Ellen Martin) in 1860 Census