What do you want to see in Italy? Even if you spent your whole trip there, with no time in Dublin at all, you'll only see a few places.
Remember that the larger the group, the slower it moves. On a 10 day trip, you can only hit some highlights; if you include Dublin for a few days, you will only be able to see two destinations in Italy (say, Rome and Venice). If you skip Dublin, you can squeeze in three destinations (say, Rome, Florence, and Venice). It will still be rushed, but doable - if you can wrangle your brood not to oversleep and miss trains! (Again, it would be rushed for a single traveler or couple, but with six, it's harder).
So, what are your (and your family's) priorities? Is seeing Dublin more important than seeing Italy? Only you can answer that. Do be sure to get input from everyone, so there's less resentment. Also prepare everyone (including yourself) for the fact that you can't do it all, and can't even do a fraction,of a sliver, of a piece, of Italy or Ireland in 10 days. I only get 10 days at a time myself, so I now how difficult cutting destinations is. But don't try to see too much, or you'll really be sorry.
A good start would be getting Rick Steves Europe Through The Back Door, which has the nuts and bolts of traveling in Europe (planning an itinerary, picking hotels, transportation, etc). Then, once you've decided on destinations, you'll want his Italy and/or Snapshot Dublin and/or Ireland books.
Our frequent poster Chani keeps kosher, so she would have specific advice for you. She's in Italy now and so may not be able to respond right away. You can start a new thread about kosher food in your destinations once you've picked them.
Both Dublin and major Italian cities have interesting Jewish histories, if that's an interest for you or your family. At least a few years ago, I read an article about how Dublin's current Jewish community was small (I think a few thousand people), but still could support a kosher butcher! Rome's Jewish community predates the diaspora; their synagogue has regular tours and there are also tours of the Jewish quarter. And Venice gave us the word "ghetto," and has multiple synagogues to visit.