My mom and i have 3 full days/four nights in Ireland. I will have a rental car upon arrival in Dublin. This is my second trip in last few years to Ireland and mom's 4th or 5th. We HAVE DONE Dublin tour, up to Drogheda, across to Galway, south to Cliffs of Mohr, Killarney, Cork, Clonmel, & Blarney Castle then back to Dublin. I'm trying to decide whether to go north from Dundalk up into Northern Ireland or head south from Dublin along the coast and Kilkenny and Waterford which we skipped last time. Thoughts???
You can't go wrong either way but personally I'd opt for the north ... heading directly to the Causeway Coast by way of the Glens of Antrim. Lots of pretty coastal scenery, hiking opportunities, and historic sites along that route. Derry is worth a side trip and, time and interest permitting, you could make a short stop in Belfast to visit the Titanic Museum.
Remember that it's a different country, so it'll be pounds rather than Euros, MPH versus KPH, etc.
And do check with your rental car provider to see if there are any special conditions (and fees) regarding taking a vehicle rented in the Republic into the North. Might be more relaxing, and cost-effective, to take the train up from Dublin, rent the car in Belfast and exploring from there ... returning the car in Belfast when you're done.
OTOH, if you haven't yet seen Glendalough, the Wicklow mtns., Powerscourt, etc. heading south would also be a great excursion for the two of you.
I also thoroughly enjoyed Northern Ireland this past March, especially Belfast (loved the Titanic Experience and the black taxi tour I took) and the Giant’s Causeway (exhilarating). If you and your Mom enjoy touring stately homes Hillsboro Castle was one of the highlights of my trip. Beautiful Georgian manor house that is used by the royal family when they are in Northern Ireland. Had a wonderful tea at a pub (roaring fire) in the cute little village after the tour, an afternoon I will never forget!