Landing in Shannon going south to Killarney then north to Donegal then to Dublin

Since your itinerary seems to be pretty well laid out already, exactly what sort of advice are you seeking?

Any sites we should see especially Sligo / donegal area.

In southwestern County Donegal, there are Slieve League (Europe's highest cliffs) with a tremendous view from the top and, in the far northwest, the even more dramatic conical Mt. Errigal. If you're a literary fan, a visit to Yeats' grave in Drumcliff is interesting. The inscription on his tombstone was, for me, worth the stop.

While in Galway I'd suggest a scenic drive around Connemara, with maybe a quick side trip around the beautiful Sky Road just west of Clifden. Continue around to the National Park for a short hike and some terrific photo ops, then a brief visit to Kylemore Abbey. We always enjoy stopping off in the village of Cong - a very scenic spot that still looks like the movie set that it was back in the 50's when "The Quiet Man" was filmed there.
From Galway there's also a pleasant day trip via the ferry from Rossaveel out to the Aran Islands (Inishmore). The company provides a shuttle (for a small fee) from Galway out to the ferry terminal. Know that it's highly weather dependent, however.
Can't help you much with Sligo, but maybe your family can suggest some local spots.
Would be real shame to be that close and not visit Derry...only about an hour from Donegal town. It's one of the most evocative places you'll visit in all of Ireland given it's history during the era of the "Troubles", plus it's just a beautiful place - with probably the best preserved city wall in all of Europe. A leisurely stroll around the ramparts takes about an hour. There's a nice little museum near one of the city gates that has some fine interpretive exhibits explaining the history of the town, as well as a fascinating display of some the artifacts they pulled up from one of the 1588 Spanish Armada galleons several years ago. I suppose you could visit Derry as a day trip from Donegal or maybe stop off on your way to Dublin.
If your ancestry traces to Ulster I'd recommend a few hours at the Ulster-American Folk Park near Omagh, and which would be along your route if you opted to drive from Derry to Dublin. Lots of interesting exhibits explaining the migration of the Scots-Irish from Ulster to the US starting in 1718.
On your way to Dublin a stop at Newgrange and the Bru Na Boinne sites would be well worth your time.
I don't recommend taking your rental car into Dublin Center. Drop it at the airport and catch a shuttle or taxi to your lodgings. You can thank me later.

I have to second Cong... it was a charming town and we had a great lunch stop there.

Definitely get rid of the car before staying in Dublin, you probably will not need it there.

Just checked on Netflix and The Quiet Man is there... time for a re-watch:)

Thank you for all the suggestions, we have been thinking of a ride to Derry so we will definitely try to fit this in. And yes our plan is to drop the car when we get to Dublin, no need to drive there. Thank you for your help.