Just because the children ended up in the workhouse it doesn't mean their father abandoned them. People were very poor and couldn't afford to feed there families and sometimes the workhouse was the only place to survive as they received food there. He also may have died and they were orphaned and put in the workhouse, there were many reasons children were there.
Rose ODonnell whose family in Ireland ended up in the workhouse was on "Who Do You Think You Are". NBC. You might
be able to find it online. They just repeated last years season.
There are books and also online information about workhouses.
Most counties in Ireland belong to a date base of birth and marriage in Parish's for details before 1864. However, Clare is not a member. I don't know how you would find records. They must have an independant genealogy office.
The Griffith Valuation is used as a census substitute
for the year 1855. There are 2 James Flaherty's listed as well as a total of 51 in Clare. There were also 21 Lee's.
If you want to find parish's in common between Flaherty's and Lee's you can cross reference them on the website.www.failteromhat.com
or better yet after getting a small amount of parish's move to www.askaboutireland.ie
watch for the Poor Law Union of Ennis.
The James Flaherty of the Parish of Drumcliff is in the
Poor Law Union of Ennis. This is where the Poor Law Union
workhouse would be located. There were more than one workhouse in each county but the residents usually came
locally in about a 12 mile radius.
There are 7 Bernard Flaherty's in the 1901 Census:www.census.nationalarchives.ie
(look to his children's names for his father,mother and sisters names and brother's names this may help you find the right one.
There are Flaherty's in the telephone book for Clare, you could write to the ones closest to Ennis, there are Lee's also from Ennis.