Hello LUV,
I realize I'm responding to a very old thread, but I stumbled across it via Google while also trying to research Thomas Feeney's family, and thought I should respond. I'm a descendant of Thomas – his son Patrick is my 2nd-great-grandfather.
I've been puzzling over the same things as you were - especially his mother. I've tracked down most of the info you mentioned, only recently noticing the appearance of Ann's surname as Rowan / Rouen.
I wanted to bring a couple of things to your attention and see what you think.
1) You probably found the 1874 marriage record for Patrick Feeney and Hannah Stoner, as it's the only document that names "Beazy Feeney" as his mother. But confusingly, there seems to be a second marriage record for him from one year later, with conflicting info. It's in the collection "Ontario, Canada, Roman Catholic Baptisms, Marriages, and Burials, 1760-1923" on Ancestry. It has his mother's name as Elisabeth Ward [?] and the bride's name as Mary Ann Stoner (I believe this had to be an error, as Hannah Stoner's mother was Mary Ann). It includes Hannah's parents Peter Stoner and Mary Ann Adams as well. The date is almost one year later, and there are different witnesses and a different priest. It's easy to imagine that this is a different Patrick Feeney, but it seems impossible with so many other similarities (same father, resides in Pickering, the ages are almost the same and the bride's parents' names are the same). Could it have been a re-do of a postponed or cancelled wedding?
2) As you point out, the 1851 census has Catherine as the first daughter born, indicating her then-age as 1 year old. But then in 1861 her age is indicated as only 4. As Eileen mentioned, there is the baptismal record that shows her birth as 19/08/1857, which corresponds more with the 1861 census age. For this reason, I believe that the Catherine in 1851 is a different person – maybe a child who died young - or it's a completely unrelated family.
3)Lastly, I wanted to point out that in the 1891 and 1901 census records, Patrick indicates his birthplace as "At Sea" and then "Ocean"! So he was presumably born during the crossing from Ireland.
Unfortunately none of this makes things much clearer, but I just wanted to share what I have in case you've found other evidence that might explain things.
I hope to hear back from you. Thanks!
Brendan