An American single-father, hoping to reconcile with his greatest love, travels back to Ireland to learn she is dying with a 10-year-old daughter who is actually his.

Firstly, the description of the father as a single father does not match the fact that he doesn't even know he has a daughter which appears at the end of the logline, unless he is a single father from another relationship not related to the one in the main plot. You may need to find another description for him. Secondly, you can give more description to why his love is actually dying (from an ailment, depression, accident, whatever). Finally , i think the plot needs more goals. After his discovery, what happens? Does he want to back out or what?. All this will keep the reader interested in finding out what happens next.

Okay, good. That's act one. And then what?

Don't mean to sound facetious there, but I think you need to give some sense of what's going to happen. Reconciliation, I guess - but where's the conflict? Does he want to adopt daughter, but she, or mother, opposes that? Does daughter want to be adopted, but he doesn't want the responsibility? Does he have to prove she's his? Try to prove she's not? All very different movies...

So can you give us a sense of the action and conflict of the movie in the logline?