We are big fans of taking our girls to pubs both in Ireland and the US. Thanks to Irish Central for this great article about pub etiquette. Love the bit about children!
Especially in rural areas, where there are music sessions on, the pub is a place that all the family enjoy. So dont bother complaining to the barman if you see kids running around the place.
That said, don't let your children act like complete hooligans. My girls love to dance, sometimes they have even been invited on the stage to sing. Just like anywhere else, you want your children to be a joy to others.
My friends at Irish Fireside have a great list of pub tips that may aid your travels.