There's an excellent motorway from Dublin airport to Cork and Galway that gets you to either in a little over 2 hours,so you might just use Dub?
You won't be tired after a 1hr flight from London so I'd drive from Dublin to your first hotel in the west/south.
At the end of your trip,just do your Dublin (and Wicklow) leg so a short hop to Dublin airport for back to London.
Better choice of cars at Dub too obviously.