Hi Jane,
I think I may have found a link in the chain for the Kavanagh family line.
I located in the Wisconsin death records a transcript for Mary Kavanagh born December 24, 1809. According to the transcrip her father was Wm Culben the original document is not shown, but I assume there probably is a transcription error.
Using the father's name of William Cullen, I was able to locate a baptism record for a Mary Cullen. It did not give a date of birth, but did list parents of William and Mary Cullen. She was baptized on April 1, 2010. If this is the same person she would have been nearly 4 months old. This is a link to the record. https://registers.nli.ie//registers/vtls000633511#page/64/mode/1up
She died October 2, 1887. She is buried in St. Martin Tours in Franklin, Wisconsin. Here is a Findagrave.com link for her grave. There are links on the page for John Kavanagh who shares a marker that is very difficult to read in the picture. There are also links for many of their children including a daughter Catherine Kavanagh Hogan. I believe you are interested in the Hogan line. There are a ton of Hogan relatives also linked to Catherine Hogan.
This link is a picture of James Kavanag and his wife, then my great-grandmother Bridget Kavanagh Wall and Catherine Kavanagh Hogan. The person who has taken the picture seems to have some knowledge of the Kavanagh family. Clicking on his name gives a link to him. I have not contacted him yet.
https://www.findagrave.com/user/49294017/photos/m?page=1#memorial_14490…
Hopefully, I was able to provide some information that is new or at least a picture of an ancestor. I feel about 60% confident in the baptism record for Mary Cullen being the right one. I'l continue to research before accept it as fact.
My email address is wall.daniel.r@gmail.com. Feel free to contact me directly, its a bit less cumbersome than this system.
BTW, what is your relationship to John Kavanagh and Mary Cullen? They are my great-great grandparents.
Good Luck
Dan