I don't think that it is too late. Some of the hotels that you are interested in or b&bs that you will see suggested on these boards may be booked but I am sure that you can find accommodations.
We did 2 weeks in the summer of 2016 and did the South. Kids were 8 and 11 at the time. As much as I would have liked to include the North, I just did not feel like we could do it all and do it well.
We rented a car and I highly recommend that. We upgraded to the automatic and it was well worth the money. No need to have a car for Dublin. We picked it up on our way out of Dublin
This was out itinerary
Dublin for 3 nights: Kilmainham gaol ( highly, highly recommend, pre-purchase tickets online as they seem out fast), St patrick's cathedral, hop on and off bus, Dublinia, Trinity College and book of Kells
Kilkenny 1 night: Kilkenny castle and walked the medieval mile. On our way out of Kilkenny we visited the Dunmore caves. It was amazing
Killarney 2 nights: Out of way from Kilkenny to Killarney we also did Blarney Castle. I know many poo poo it but we really enjoyed out time there. In Killarney we rented bikes and biked the National Park, did a jaunty car ride, did a sheep herding and shearing demonstration at Kissane Farms There is some amazing hiking in and around Killarney
We also drove the Ring of Kerry which was amazing.
Dingle 2 nights: drove the Dingle loop, visited the town and did the behives. Great hiking here too as well as horseback riding and kayaking.
Galway: 2 nights. Cliffs of Moher, On our way to Galway, we also stopped at Bunratty Castle and Folk park
Ashford Castle: 1 night ( we stye dat the Ashford lodge which is on the same property) We did horseback riding, archery and the awesome hawk walk here. Absolutely amazing. We still talk about it 2 years later.
We then dove to Dublin stayed by the airport and flew home.
This forum is great to get some ideas as well as tips and tricks for your travels.