Ireland in February, 2 teens with me driving, start/end Kerry airport? Skellig Michael?

Cliffs of Moher are open then. The Arans have ferries year round but much is closed on the islands at that time of year. If you contact one of the B&B 's they can advise specifics. Skellig Michael as far as I know has no tours then. The non landing eco tours kick off in April and Landings in May. I might be wrong but that was our experience. Still fun stuff to see and do.....like the Cliffs of Kerry etc but many smaller towns restaurants and cafes aren't open......stuff will be open but selection will be limited. Good luck ....still so much to enjoy !!!!!

With only 7 or 8 days at your disposal you really need to prioritize in order to keep from running yourself ragged trying to see everything on your list, and I'd start by selecting either Galway or Cork...but not both. You just don't have the time.
You could easily spend all of your days exploring Killarney, the Ring of Kerry, the Skellig Ring Road (highly recommended), Killarney National Park in general and the Gap of Dunloe in particular, the Dingle peninsula, and Beara. Then maybe work your way back to Dublin via the town of Cobh. A stop at their Heritage Center might be of interest to you and your kids since it's likely that your grandmother emigrated from that port - it was called Queenstown back then, and was the Titanic's last port of call before heading west and her date with the iceberg. Their Titanic Experience museum might be of interest, and the little town itself would make a good stop for lunch.
Returning to Dublin, a drive thru the Wicklow Mountains along the old Military Road is quite scenic, and a stop at the monastic settlement at Glendalough would be time well spent.
On the other hand, Galway and Connemarra are terrific. The ferry over to the Aran islands runs year round and is only dependent on sea state - you can check the forecast the day before and then just walk up for tickets. Dun Aengus is the big attraction, and there will be vans and jaunting cars lined up on the pier as you disembark offering tours of the island.
While we love the Beara peninsula and always recommend it, I'm not sure that going all the way out to the Dursey Island cable car would be the best use of your time unless you're avid hikers and want to spend most of a day exploring the island in order to experience first hand the impact of the famine years on West Cork.
As you say, the short days and the likelihood of some rainy days will likely put a crimp in some of your outdoor plans - all the more reason to slow it down and plan a more compact itinerary.
Safe travels.

Thanks so much for your helpful feedback! I am now reconsidering the plan to eliminate Dublin this round and fly in/out of kerry airport. Hopefully this will give us a little more time to explore and some down time as well. A bit bummed about the fact that I’m limited with the month traveling and no skellig your at that time. Although I’m sure my kids won’t care either way-they’re not as adventurous outdoors as I.

1) Kerry Airport is fantastic! I fly out next month for a trip to Washington, DC.

2) - IMPORTANT!!! Skellig Michael is not accessible in the winter! The season to go on island ended October 2nd. The Skellig Experience visitors center on Valentia Island is a fantastic place to go, see tons of info, movies, photos, and then see the islands from numerous points in the area around Valentia, Port Magee, The Glen, the hill to Coomakista. The Kerry Cliffs are a must - trust me the kids will like them BETTER than the Cliffs of Moher. Everyone I've brought there says that.

3) I stay in Killarney twice a month. It's a big town; if you want small village in Ireland feel, I suggest Port Magee (at the bridge onto Valentia Island) or Knightstown on the Island. Both places have accomodation open in the winter!

Enjoy the Skellig Coast region!

Susan - ExPat in Waterville