Sounds like a fascinating school - do you play already?
For your trip - on balance I'd recommend going after the school. Reason being the school holidays in Ireland end at the end of August. As your trip would extend into early September the places you might like to visit will be a little less busy and better value. Also - this is a little Irish secret... the best weather of the year seems to be always when the kids are studying for exams in May & June and when they go back to school in September. September weather is often the best of the year.
A couple of important decisions:
1) How do you like to get around? Renting a car gives you lots of flexibility but some people get a little nervous about driving on the opposite side of the road. The Dublin-Sligo road is excellent & very easy but between Clones & Sligo & around the Wild Atlantic Way things get tighter. You can take your time, stop & start, so it's never a problem just something to consider. If getting someone else to drive you around is what you'd like I'll list some tour operators who do a really nice job of looking after you.
2) How active would you like to be?
For example, a couple of hours from Sligo is Achill Island which has the 'Greenway' a really lovely cycle path on the Wild Atlantic Way. It's not very tough but requires a little effort. You can rent pedal bikes - and ones with a little electric help :)
Alternatively - between Clones & Sligo you'll be near Carrick On Shannon where you hire a boat to go cruise on the river Shannon. Again it's a little effort but a fantastic experience. My wife and I did it two years ago with no experience and it's just great. If outdoor activities aren't your thing - think about Irish music sessions in pubs or some food experiences. I'll put in a couple of links below.
* CIE Tours - have been bringing people to Ireland for ages. Here's a list of their tours
* Vagabond tours go off the beaten track & do a lovely job here
* Hire a boat to cruise on the river Shannon - both relaxing and active at the same time
* Mulranny Park Hotel
is on the Wild Atlantic Way and the Greenway - you can rent bikes from here too. This is an excellent location actually. Driving on the coasts of nearby Achill Island is amazing - I took thousands of photos here.
* The Ice House Hotel
gets *lots* of recommendations. I've been told I'm going there soon
* On September 4th the All Ireland Hurling final will be on in Dublin. I was at the 2013 final with 80,000 other people - I felt like we were right at the heart of Irish life at that moment - the President & Taoiseach (Prime Minister) are there. The game is two thousand years old and it feels like you're living history too by watching it. Tickets become available later in the year on the GAA website
* In Dublin, if you can, book Locks Restaurant
- it's really great. There are quite a few good restaurants but I like that one.
That's a few tips - I'm sure a few more will occur to me after I stop writing. Enjoy your planning as much as your trip!
All the best,