Although there are no hard and fast "rules" in this area, it is normal to seat small children with their parents providing you arrive in plenty of time for check-in. (ie If check-in is advertised as being up to 60 minutes before departure, if you have special requirements (eg seating together requests, excess baggage to negotiate, wheelchair assistance etc) you should really aim to be there at least 90 minutes before departure).
Although you say you arrived at check-in in plenty of time, the Boarding Pass will bear a "Sequence Number" showing the order in which passengers checked in. Therrefore, regardless of what time you arrived at the airport, if the other 150 pax on your flight checked in before you, there's not a lot can be done I'm afraid. (It's simply not fair on the other passengers to start juggling their seats around just because you couldn't be bothered to get to the airport early enough!) Most airlines do not pre-assign seats on Short Haul flights, although we will do our best to get you together if you play ball with us and arrive in plenty of time for your flight!
Speaking from BA's point of view, since "On-Line" check in was opened up, seating families together at check-in has become more and more difficult. If
www.aerlingus.com has "On-Line" check in, why not give it a try next time you fly?