With the euro exchange rate, you'd be better off in the South. I mean Antrim's OK - the Glens and the Giant's causeway, but there it is, on the far North, with all the rest of the quite heavily populated North to travel through before you see anything nice again.
I'd head to the South, and to the West.
Also I'd forget totally about a pool - if it stops raining you can go swimming in the freezing sea - or even if it's raining - it's all water after all.
Surfing schools are fabulous for the kids as they have wetsuits as well. We love the one in Fanore, Fanore Surf School, in Co Clare on the west coast, a little bit south of Galway city.
Ireland is a place to slow down, not gad about looking at the sights: you may find the pace a bit slow in one place for two weeks so I'd advise two places.
Galway is lovely and has an arts festival at the moment
and Cork is warm - think Devon in temperatures.
Donegal is wild and coldish
Mayo is like a deserted Lake District.
Waterford is dryer (ish) Wexford like Somerset.
Basically the weather is shite, rain rain and more rain, but you don't come to Ireland for the sunshine.
Kick back and spend some time with yourselves. Bring some cards and board games! Enjoy the scenery and look for some workshops / arts and crafts things to do. Lots of horse riding too, especially in Sligo (Sligo equestrian centre), again west and north a little bit of Galway.
For accommodation have a look at Special Places to Stay, and the Irish Tourist Board's website: Discover Ireland.
Have fun!