Dublin for 2 days

The Rick Steves Ireland guidebook has suggestions in the Dublin chapter ranked by stars (the more stars, the more attractive the sight/activity). I would say to start there, using your own judgment about what is most suitable for your kids. We had about 48 hours on the ground in Dublin and followed this list, and really enjoyed everything we did.

Dublin is a city where the hop on hop off bus works well. Then pick the sites from among the stops.
Killmainham Gaol is a must, book tickets ahead.

The Viking Splash Tour looks really corny but the kids love it - apparently so do the adults. Dublinia is a very hands-on museum, fun for all ages, and a good look at the real Vikings and the Middle Ages, so it's probably better to do the Splash Tour first.

When I took the Literary Pub Crawl, there were a few kids and they seemed to enjoy it. The guides are very engaging. It's definitely great for adults.

We all loved the National Museum, which included the bog man---one of my favorite things to see in Dublin!

Darlinda is referring to the National Archaeology Museum, which is a wow and free to boot.

Get the 48 HoHo Bus pass, book for Kilmainham Gaol and make a stop at Dublin Castle.

Get a guidebook for the kids to look through together - the 15yo will certainly have ideas and can help the 10yo as well.