Even though you can't visit Ireland until next year, you can visit the web site of the GRO ->
http://www.gro.ie/fees.htm. The Cavan office has been very helpful to me in the past. (Addresses and phone numbers at the bottom of the page.)
I suspect that the marriage record you found at the IFHF site also had a Parish/District included. That's a clue as to where Kate likely lived, since they probably were married in her Parish. You could request the civil marriage record from the GRO since you know the date. They're pretty good at searching. It may not get you more than you already have, but you don't know without seeing it. It might at least have their ages. Older records sometimes just say Full Age or something to that effect, but hopefully an 1898/1899 record will have the ages.
You could also try for Kate (Catharine's) birth in 1873'ish, father Philip, mother unknown, but it might be better to hopefully confirm the age from the marriage record first.
Regarding your mother, aunts and uncles... My father, aunts and uncles all swore that my Grandfather was from Ballinamore, Co Leitrim. I finally tracked down his birth record in Bawnboy, Co Cavan. My GGrandfather was a baker who also moved around quite a bit. There were 5 children born in Arda, Bawnboy, Crossdoney and Granard. Eventually the family settled down in Ballinamore, when my Grandfather was about 15, but he never actually lived there. He was working with an uncle on the family homestead in Garrymore. So don't let family lore get in the way. (btw, full disclosure, the GRO could not find a marriage record for my GGrandparents although I did find the church record info at IFHF.)
Good luck.
John