Hi,
Thank you for your message.
Civil registration began in IReland in 1864, so as Ellen's death would have occured after this there should be a civil record of it. Civil Registration records are available from the General Register's Office. You can access the website here: http://www.groireland.ie/research.htm
A useful website in terms of geneanlogy tips is Genealogy toolkit. For their information on death certs follow this link:
http://www.irish-genealogy-toolkit.com/Irish-deaths.html
You could try looking for Patrick's father Thomas in Griffith's Valuation. This was a property valuation survey carried out in Ireland between 1848-1864. Although it offers no genealogical information it does give the name of the parish a person lived in. Depending on how many results are returned for Thomas, you may be able to find the parish that he lived in. You can then use this information to check the relevant church records. You can search Griffith's Valuation here:
http://www.askaboutireland.ie/griffith-valuation/
Some other websites which may be helpful are:
The National Archives of Ireland http://www.nationalarchives.ie/genealogy1/genealogy-records/introduction/
The National Library of Ireland http://www.nli.ie/en/family-history-introduction.aspx
The Public Records Office of Northern Ireland http://www.proni.gov.uk/index/family_history.htm
Family Search: https://familysearch.org/
Genealogy Links: http://www.genealogylinks.net/uk/ireland/westmeath/index.html
You could also try contacting the Westmeath genealogy centre for possible assistance. However, a fee may apply. Here are their contact details:
Dun na Si Heritage Centre,
Knockdomney,
Moate,
Co. Westmeath.
Phone: (090) 6481183 EMail: dunnasimoate@eircom.net
I hope that this is helpful.
Kind regards,
Genealogy Support