Old Head and Cork are not really SW Ireland...
If I were you I'd drop them all together, I find the West coast courses are superior to those two. OK old Head is dramatic, but not a great course. Also always have better weather on the west coast.
And if you don't know the Irish roads...it might waste a lot of time!
The suggestions to play twice the best ones are by far the most sensible. Play both Lahinch yes, and both Ballybunions too if you can for the fabulous views and fun of Cashen rollercoaster. You won't forget it. It makes sense to minimise the transfers too.
Same applies for Tralee, you might even want to play it twice, as the back nine knocks you out first time, you don't know how to play it and it can leave you frustrated. Some of the best views there too. Unforgettable.
For Tralee and Cashen, just leave the scorecards in the bag...or play a friendly team format.
Castle Greggory is cool and in a beautiful setting.
Dooks is a good choice, old style, quaint, marvellous; and if you have a bit of time, take the road across the mountains for Waterville. Stunning.
Forget Ballyheigue. And yes Killarney is a nice setting, but not as good as the others. The weather changes quickly on the coast, but because of the MacGillycuddy's it can be very wet inland...
And near Tralee book yourselves into the Oyster Tavern, fresh fish aplenty!
Have a great trip