Hi Jess -- I was in Ireland for 12 days in September of this year and for about eight days a year ago, so I can definitely give you my thoughts based on my travels there.
On my most recent trip, we spent two nights in Galway. In my opinion, Galway isn't worth it except if you use it as your base for traveling in the area. It's just a big city without (in my opinion) anything really worth seeing. I recommend that you spend an extra day in Dublin instead if you want the "big/bigger city" experience. Dublin is definitely far more interesting than Galway is.
If I were you, I'd skip Galway and drive from Ashford Castle through Galway to the Cliffs of Moher on the west coast. Spend a night in Doolin, which is just a few miles from the Cliffs of Moher. Doolin is a wonderful little town and has several great B&Bs. We stayed at Daly's House and loved it. By staying in Doolin, you can get to the Cliffs of Moher in the mid to late afternoon and not feel rushed to get somewhere before dark. And if the weather that afternoon isn't the best, you have another chance to visit the Cliffs the next morning so that you give yourselves a better chance of seeing the Cliffs in good weather.
I also highly recommend that you consider spending three nights, not two, in Dingle. Dingle is my favorite town in Ireland and I LOVE staying there. I've stayed for three nights during each of my two most recent Ireland trips and never thought that I'd stayed for too long. Dingle is small, yet full of great music and good food. While you're there, make sure to visit Tommy O'Sullivan's Court House Pub during at least one evening, if not two. It's a great little pub with local musicians every night. And if the weather is nice, make sure to drive the Dingle Peninsula one day while you're there. I suggest letting Tim Collins take you on that tour, as the roads on the peninsula are very narrow at times (not fun to drive yourself). His number is 66-915-1606; my B&B host called him to arrange for him to pick us up at our B&B. He charged €20 per person and there were about eight people on the tour we did with him.
I've driven through Killarney but never stayed there. From what I've seen on these message boards, Kenmare might be a better place to stay. It's apparently not as touristy as Killarney. I've stopped in Kenmare for lunch on two different trips while driving from Kinsale to Dingle or vice-versa, and have thought that I'd like to spend a night in Kenmare on a future Ireland trip.
As the previous poster suggested, you might want to fly out of Shannon instead of Dublin if you can because it's a shorter drive from Killarney, although there's nothing wrong with spending one last night in Dublin and flying from there. Just keep in mind that even without stops along the way, it can take several hours to drive from, say, Killarney to Dublin. As the previous poster mentions, the days are shorter in March so it gets dark sooner. I highly recommend NEVER driving in Ireland while it's dark! It's difficult enough in the daylight.
If you do fly out of Shannon, consider spending your final night either in one of the airport hotels or in the little town of Bunratty, which is just a few minutes' drive from the airport.