7 nights in Ireland- intinerary which includes Cahersiveen

You're spreading yourself pretty thin here, especially assuming that your 7 nights equals only 6 days for touring.
Doing the trip as an open jaw, ie flying into Dublin and flying out of Shannon (or the reverse) would preclude having to backtrack to catch your departing flight. Having a car will allow for maximum flexibility in getting around, although you could go by train between Galway and Dublin.
Maybe a couple of nights in Dublin upon arrival - just to settle in and get over jet lag. Then train to Galway for a couple of nights, pick up a car for local explorations around Connemara and for the trip down to Cahersiveen and the ROK, then returning to Shannon for the flight home.
You're really going to be pinched for time no matter how you organize it, but that might make the most of the time you have.

I love Ireland! I recommend signing up for the "Literary Pub Crawl" while in Dublin, it is a great evening. After a couple of nights in Dublin I would drive to Galway and Cahersiveen and see the family roots, etc, then plan on spending two nights at Ashford Castle (truly amazing experience), take the Falconry Class while there and soak in the beauty of Connamara Park. Then head to Bunratty (next to Shannon) and attend the Bunratty Castle Medieval banquet (great food and music) . I know you will miss Dingle and the Ring of Kerry but I think your time restrictions will make it difficult to cover that much territory.

Important: what ever the mileage your trying to cover in Ireland you should double the time that you think it will take.

Thank you for all the suggestions, I spoke with my daughter and Galway is not a must, however the Rock of Cashel is for me. Does that change anyone's itinerary ideas.

Skipping Galway on this trip will certainly make it more relaxing for both of you, and will allow you to concentrate on one of the prettiest parts of Ireland.
Cashel will be an easy enroute stop on your drive from Dublin to Kerry.
Basing yourself in or near Cahirciveen for a few days will allow you to savor some of the highlights in the area. Other than driving the ROK loop, another possibility would be to visit the Skellig Center in Portmagee and maybe take the boat trip out to Skellig Michael. The Skellig Ring road is a short spur off the ROK that has terrific views of the islands from the headlands if the weather cooperates. The Gap of Dunloe is one of the prettiest glens in Ireland, and the 3.5 mile walk (each way) up to the lookout point at the end is one of the most picturesque. The jaunting cars can be fun too.
Killarney National Park, Muckross House, and the other attractions on the other side of the lake might interest your daughter as well.
A couple of days in Dingle would be worthwhile, both to meander along the Slea Head Drive and to enjoy the relaxed ambiance of the town in the evening after the tour buses depart.
Depending upon your departure time from Shannon you might want to drive up there the evening before to save yourselves the stress of traveling to make your flight that day. Bunratty would be a good choice. Then sleep in a bit the next morning, have breakfast, drop off the car and be on your way.
Good Luck.

I can't thank you enough for your suggestions, however..... we have made reservations flying into Shannon and out of Dublin. Why? a coin toss. Not sure if this was the best idea but it's done. When we land in Shannon would it be too far to see the Cliffs of Moher (know we will be tired) and stay someplace around there possibly Ennis. I know I will be backtracking would like to go to Dingle, Cahersiveen, Kinsale, Rock of Cashel, ending up in Dublin for 2 nights. Any other must see sights plus itinerary ideas would be great.