The Ireland being described (Third World?) is not the one I am familiar with. Yes there are expenses you do not face in Britain (health, childcare depending on your work situation) and you may find living is more expensive depending on your taste. But getting around is incredibly easier than it used to be.
I agree 100% with SophySinclair -- children get a better grounding in the basics, and the secondary system (if you end up staying that long) has much to recommend it, with its general education requirements and no early specialisation. Everyone who is university bound does maths, English, possibly Irish, another language, sciences, history/geography, econ, possibly art or music (and there are more). It is a more rounded education than the education Britain offers. More children go on to 18 at secondary.
Living in Dublin is lovely if you choose your area well, just as in any other city, and schools tend to reflect the educational priorities (or lack thereof) of the local residents. There are definitely some areas that are far more desirable than others and they are priced accordingly. In country areas you won't have the same pace of life and you may find yourself in a more homogenous community. A cousin who moved out of Dublin several years ago loves where she is and her children settled in and thrived. My own niece is in school in Dublin city (a private girls' school) and is doing very well there -- if you have time, investigate thoroughly before you choose where to go. I have one cousin who does a 1.5 hour commute to Dublin from a south east county every day and back every evening. He and his family like the life in the country and the local national schools and secondary options.
If you choose Dublin, I would avoid in no particular order Tallaght, Crumlin, Blanchardstown/Clonsilla, North City Centre/Sheriff Street/North Wall, parts of Clondalkin, Ballyfermot, Coolock, Finglas, Inchicore, Kimmage, Santry, Dolphins Barn-Rialto, Darndale, Ballymun, Ballybough, Corduff, Ballybrack, Sallynoggin, Ringsend, Jobstown, Kilbarrack, Donaghmede, Chapelizod, Mercer Street-Cuffe Street, Ballyogan, parts of Firhouse, Mulhuddart, Walkinstown, Cabra, Drimnagh, Neilstown, Bawnogue, Islandbridge, Cherry Orchard, parts of Ballinteer, Killester, Donnycarney, Mounttown-DunLaoghaire, Raheny, Balally, Bluebell, Balcurris, Poppintree, parts of Churchtown.
OTOH, Glasnevin, Drumcondra (parts), Clontarf, Malahide, Sutton (parts), Skerries, Rush, Lusk, Castleknock, Portmarnock, Bayside, Howth, Baldoyle, Ranelagh, Blackrock, Foxrock, Ballsbridge, parts of Killiney (some parts of Killiney are actually Ballybrack), Dalkey, parts of Shankill (some parts are Ballybrack south), parts of Cabinteely (runs into Ballybrack on the south east), Donnybrook, Milltown, Dundrum, Clonskeagh, Leopardstown, parts of Stillorgan, Terenure, Sandymount, Belfield, Booterstown, parts of Monkstown, Rathfarnham, Templeogue, lots of Knocklyon, Rathmines, Rathgar, parts of Glenageary, parts of Dun Laoghaire, Sandycove, area between Bray and Shankill are all nice. D18, D4, D6 in general. Maybe Swords.
Have probably overlooked a lot. Apologies to anyone with a soft spot for any of those places I would avoid.
Though some parts of Dublin 8-Phibsborough-Stoneybatter-Liberties/Coombe-Smithfield have improved I would still not fancy the urban pioneer experience in the city with children unless in the heart of D2/Leeson Street/Baggot Street areas (but avoid Pearse Street) and even then you would be looking at private schools. Maybe Portobello...but again, children need to go to school.
Outside of the city, Celbridge (has a rep for drugs though), Maynooth, Lucan (or is that in Dublin??), Newbridge, Naas, Enfield in Kildare; Laytown, Bettystown in far north Dublin; Navan, Ashbourne, Dunshaughlin, Trim, Slane in Meath; Arklow, Bray, Greystones and Enniskerry (and other northern Wicklow towns), Carlow town or other small towns in north Co. Carlow might be possibilities with a bit of a commute.
The south side allows you faster access out to the Wicklow mountains -- lovely coastal spots south of the city too with lots of walks and getting out in the fresh air opportunities.
People are a lot more 'personal' with you in Ireland than in Britain. That goes for petty criminals as well as nice neighbours.