Just a poll. More info later, but I don’t want to poison the poll results right now.
Kate-lynn
If I’m in Ireland, I know it’s “Kathleen”. If it’s an American girl, she’s probably “Kate-lynn.”
The two girls I’ve known by that spelling were called “Kate-lynn.”
Not beeing from English speaking country, so not very much Caitlins around. So i’ll go with Kate-lyn based mostly on Hwood and other 'murricas media servers.
Wow. Poll results are overwhelmingly in favor of Kate-lyn here.
So the story - the wife and I were thinking of names for the tabbykit and Caitlin was one of the names that came up. We really like Kate-lyn, with the spelling of Caitlin, but found out that the Orish way of pronouncing that name sounds a lot more like Kath-leen, which we’re much less hot about. And so I turn to the dope. 
This is kind of the opposite problem we had with our first choice, Siobhan, in which we attempted to Anglicise it a bit by spelling it Shevonne. Consensus was that that was a terrible idea. But if everyone pronounces Caitlin Kate-lyn, then I think we’ve got a winner!
Thanks all.
Upon first reading the name I said “Kate-ill-in”, three syllaballs and and all
Since I now realize there is no other I in there (like I thought/normally see in that instance) I changed to “kate-lynn”
So my poll answer of “smoething else” still stands
Kathleen.
I’d pronounce it however the person told me their name was pronounced (honestly, not trying to be a smartass). In the U.S. at least, 9 out of 10 people (or more) will pronounce it kate-lynn by default. Your daughter might have to correct someone’s pronunciation in the random instance, but that’s true of a lot of names and isn’t a big deal at all. I don’t think you have anything to worry about.
Throatwarbler Mangrove.
Ok, Kate-Linn.
My daughter is Caitlin, pronounced kate-linn.
I was told by a dedicated student of Celtic languages that the native, traditional pronunciation is closer to “kaysh-leen” than “kath-leen” or “kayt-leen.”
How often do you anticipate having to write your cat’s name? Probably not often at all, I suspect. However you pronounce it is how everyone else will hear and pronounce it as well. I don’t think anyone is going to ask you how you spell it. Non issue.
If I’m reading between the lines of the OP correctly, tabbykit is a (soon-to-be-born) human child. If that’s true, I imagine Tabby_Cat and his wife will be writing whatever name they choose quite regularly. 
Yeah, I thought he was literally talking about a cat until I re-read the OP.
Sort of like Cal_Meacham and MilliCal.
The only Caitlin I know pronounces it Kate-Lyn.
I met someone in college who wanted it pronounced “Cat-lynn” but otherwise it’s always been “Kate-lynn”
Here in Ireland it could be Kathleen or Cawtch-Leen if it has the fadas, Cáitlín, and IIRC the American pronunciation has made inroads too.
It’s just the Irish spelling for “Kathleen,” which in turn is the Irish version of Katharine. The trouble is, Irish palatal T is not directly equivalent to anything in other dialects of English. In earlier centuries it was mapped onto TH (thus the spelling). For Cait, the T is more like English CH, but not quite: even more like T in British English Tuesday (Tyooz-day). In the combination -itlí-, it’s still more like TH to my ear (rather than An Gadaí’s “Cawtch-Leen”), but nothing like the TH in English Kathleen.
I always use this pronunciation when I call roll, and I am always corrected to “Kate-lynn.”
I feel like an idiot. I’ve always pronounced Caitlin as “Rory”.
Ignorace fought.
It’s a coworker rather than a classmate, but exactly this otherwise.