Cork City as a Base

Just my 2 cents: March weather can be notoriously fickle in all of Ireland and especially Cork. Spring will still be just a distant promise so you'll be dealing with cold temps, short days, and a lot of rainy conditions. Point being that you might want to consider throttling back on your pace bit to allow for those days when doing much of anything outside really won't be an option.
Personal opinion only, but I think 4 days in Dublin is a day or two too many. A couple of days in the city will be enough to get over your jet lag and generally satisfy your curiousity about the place.

Rather than using up most of another travel day just getting from Cork to Galway, my suggestion would be to base yourselves in the vicinity of Killarney for a few days - long enough to enjoy the National Park and the Ring of Kerry. Dingle would be only an hour away, making a day trip there much more doable than trying to do it from Cork. And if you'll have a car you could explore the beautiful Skellig Ring road with a stop at the Kerry Cliffs, as well as enjoying a few hours at the Gap of Dunloe - one of the prettiest little glens in Ireland.

Personally, I'd devote the majority of my time to the west of Ireland, ie Dingle and Kerry, rather than trying to make it all the way up to Galway this trip.

We stayed in Kinsale in March and liked it there a lot. I don’t recall much about Cork at all and we spent a day there.
We drove all over Ireland and although there was some rain, it was a great trip and we were able to be outside most of the time.

Although I'm sure some people would disagree, I don't think Cork City is all that nice. I much prefer the West coast of Ireland. I don't go to Ireland for the cities as much as for the scenery and the small towns. Having said that, Galway is a great but probably not for 3 to 4 nights. And I agree that Dublin probably doesn't warrant 4 nights. Due to the time it takes to cover distances on narrow roads, I personally don't think staying in one place and doing day trips is a good idea in Ireland. You spend a lot of time backtracking. I think you are better off staying at a B&B for a night or two and going from place to place. If you really want to stay for a few days, you might consider Kenmare a small town that is easy to get in and out of and is fairly convenient to the most scenic (in my opinion) parts of Ireland - Beara Peninsula, Dingle Peninsula, Ring of Kerry.

Cork is not worth much time, if any, on a first trip to Eire. A good central base would be Clifford's B&B in Waterville. Or Butler Arms Hotel in Waterville if you want to splurge. Both are right on Ballingskelligs Bay. Not a bad place to begin and end the day.