Was SULLIVAN your great-grandmother's maiden name?
What is your source for the information that Kathryn was sent to an Ursuline Convent?
Do you already know her parents' names and where the family was living as of the enumeration date of the 1870 census and/or when Kathryn was born circa 1871?
What was the name of the probable sister you've located in the 1880 census in CedarRapids, Linn County, IA?
Your post suggests that Kathryn's father died sometime between 1881 and 1884. Have you tried to locate a death record or obituary that might make reference to a parish to which the family belonged?
If you don't already know Kathryn's parents' names, and if she and/or her probable sister resided in Iowa in 1925, the state census may list their parents' names and state/country of birth.
Research in historical newspapers may be helpful. If you need assistance, contact me via email and please cut-and-paste the text of this message:
maryfobian [at] comcast [dot] net