We have traveled with teens to several countries in Europe including Ireland and have always experienced the same as you are finding. Family rooms if you find them listed (not super common) are a double-sized bed, sometimes a queen, and one twin or single-sized bed. I have yet to see rollaway cots as an option when I searched for my family, you may need to follow up directly with the establishment. I don't think that is a common practice there. We actually had better luck in Ireland though compared with other countries we've visited finding one room for all 4 of us.
For our family of 4, often we have had to reserve 2 rooms which I then follow up with the hotel directly to ask that the rooms are next to each other (or if they have adjoining rooms). Granted my kids are older so that won't work for you now but something to think about for future family travels overseas.