There is a bmd website for Westmeath, where you can put both parents names in the search. I did find your
Patrick 1 ox 12 in 8 Parishes in the Griffith Valuation of 1854. This is a fee based service that have just added some passenger records.
Free Griffith: www.askaboutireland.ie
Patrick Connell, Parish of Mullingar, Townland of
Culleen More tenant of James McLoughlin, house, outbuildings
and land 19 acres 0 roods and 9 perches. The Poor Law Union or Civil Registration District (1864+) Mullingarwww.familysearch.org
will have any 1864+ records but the
previous version of this website has old parish records, donated records, etc.ancestral files, and the 1880/1881 US,UK and CA census. The new versions has US Census and some passenger records. The old version also allows you to search other countries for their LDS records.
There are still Connell's listed in Westmeath including some in the Mullingar area, also Dalton's. Perhaps a few letters might help?
You just google Westmeath-white pages, I know you can do the same for Australia but don't know about Argentina.
I do know Ancestry has passenger records.