Catherine,
I don't know as much about Northern Ireland, so take this with a grain of salt. You may want to consider flying into Dublin and spending two days there. I'd pick your rental up on the outskirts of town and then drive up to Belfast, seeing Newgrange on the way. You could spend a day exploring Belfast if you want to. The next day I would spend seeing Antrim Coast and Giant's Causeway, possibly drive on to Donegal for the night. You could spend the next day exploring Connemara area on the way down to Doolin. The next day you could spend exploring the Cliffs of Moher and possibly the Burren area. Each have a lot to offer and we loved them both. You could spend your next two nights in Dingle and the following two nights in either Kenmare or Killarney.
Dublin: 2 nights
Belfast: 2 nights
Donegal: 1 night
Doolin: 2 nights
Dingle: 2 nights
Kenmare/Kilkenny: 2 nights
Fly home out of Shannon.
This route (or similar, effectively uses up your 11 days. I don't think you can do Kinsale/Center Ireland (Rock of Cashel) and Northern Ireland on one trip and do justice to the areas you are seeing. There's a lot of drive time in here, too. You'd have to cut something. Perhaps cut Kenmare/Kilkenny if you are really wanting to see Kinsale. I've never been there so I can't compare the two areas.
My other suggestion would be:
Fly into Shannon
Doolin: 2 nights
Dingle: 2 nights
Kenmare/Killarney: 2 nights
Kinsale: 1 night (see Rock of Cashel/Cahir Castle on next day's drive)
Option 1:
Trim (or somewhere in vicinity): 1 night
Belfast: 1 night
Dublin: 2 nights
Option 2:
Dublin: 3 nights (guided day-trip up to Belfast and Giant's Causeway)
-- Option 2 doesn't account for 1 night. You could easily put it anywhere you feel like you'd want an extra night. I'd vote Kenmare/Killarney, but there are a bunch of people here that love Dingle and I'm sure they'd vote for that. Or you may find something else in your planning that you'd like to allocate a day for.