14 day Ireland Itinerary-Seeking advice

What a lovely trip you have planned. We didn’t stay in Cork but we did stay in Kinsale and it’s a charming village on the coast.

Re your Day 9: The coastal drive heading south from Doolin towards Kilkee is a very pretty one on a sunny day, and Kilkee itself makes for a nice lunch stop - featuring a pretty stretch of beach and a nice cliff walk that you'll probably have all to yourselves.
The Tarbert ferry is indeed a pleasant way to cross the Shannon.
Might suggest driving into Dingle via the Conor Pass ... but only if the weather cooperates. It necks down to a single lane in places and can be a white knuckle experience if you encounter rain or fog. Can preview the drive using the Street View feature on Google Maps to see what you'll be dealing with.

While exploring the area around Dingle consider a stop at the South Pole Inn in the nearby village of Annascaul - established in the early 1920"s by Tom Crean, a local boy and one of Ernest Shackleton's officers during the ill-fated Antarctic expedition of 1914. It's a convivial pub in it's own right, and is also something of a little museum featuring photos and artifacts from Crean's several polar expeditions. It's worth a visit.
Suggest getting an early start for your excursion over to the Gap of Dunloe. The tour buses start to roll in by about 9 AM, but if you arrive early you'll only encounter the pony trap drivers beginning to stage near Kate Kearney's. The hike/walk to the head of the glen (about 3.5 miles one-way) is gorgeous, and there's at least one little tea room along the way if you fancy a cup of coffee and a scone.
I agree with the suggestion to stay in Kinsale versus Cork.
Appears to be a well thought-out itinerary.

Day 3 is a busy day as it is 3.5-4 hours drive depending on traffic. Make sure you book Newgrange in advance as it gets busy and tickets soon sell out. Yoiu need to allow a morning for this as as well as Newgrange there is also Nowth (very different, but also worth seeing if time allows) as well as the exhibition in the visitor centre. Trim could also take another couple of hours too.

I would definitely add Kilmainhaim Gaol in Dublin but just book ahead of time. I think if takes a little more than an hour for the guided tour. Have been there three times and never stops amazing me. I think it is best site in Dublin. Book of Kells were okay. Walk by the GPO and also include walk over Halfpenny Bridge. Enjoy Ireland. It is more than fantastic!

Not far from Athlone on your Day 3 drive to Galway is the monastic site at Clonmacnoise - an ancient and evocative historic site on the River Shannon. It's much less crowded than Glendalough and is a pleasant place to explore for an hour or so. It's easy to imagine Viking long ships coming up the river to raid the place in the 10th century.

Renting a car from one of the airport concessions is probably your best option - a bigger selection of vehicles plus it's pretty easy to get onto the M50 motorway and on your way from there. There are a couple of places along the South Circular Road outside the city center that might be worth a look too - would be much closer to your hotel at any rate, and getting out of town from there looks pretty straightforward. Their operating hours are a bit more restrictive than the offices at the airport however.
Be aware that the airport rental car lots are located along Swords Road about a mile from the terminals ... you'll want to ensure that your taxi driver knows where to drop you.