Hello Shana, warm greetings from Ireland.
I have gone around Ireland both clockwise and counter-clockwise (we Irish say anti-clockwise FYI!) hundreds of times in 20 years guiding tour-groups.
Years ago I wouldve mildly suggested not to go counter-clockwise as Belfast in the old days was quite a sobering first impression of Ireland for my guests.
Thats totally changed now though, and Belfast is all Titanic, Game of Thrones and trendy coffee shops! So its a wonderful first impression. (I must stress too that the political and religious divisions still simmer big-time in certain areas and are never too far from the surface, should you wish to seek them out, which I strongly encourage you to do, but my point is they are no longer on the surface and you could walk through Belfast city-centre on a sunny day with an ice-cream and not realise anything and ever gone on there)
So have no fear in re-routing your plans and going 'the other way round'. You'll be grand!
Slainte/Good health
Stephen McPhilemy
Rick Steves Ireland Tour-Guide
Dingle and Derry