When we took the train tours, there were then private buses to meet us at the other end, so we were able to go everywhere the tour was designed to go. We haven't missed seeing much in Ireland, because the tours are set up to get us where we wanted to go. That said, the cost of the tours might make it too expensive for a large family. We did get to see stuff that we would not have seen if the tour companies hadn't made arrangements to get keys to open more private places.
We have had kids with us on most trips to Ireland, including Dublin, and they loved it all..the old castles, the old jail (kids loved it), the street activities, and of course the touring throughout Ireland (especially eating and sleeping in a real castle..that was their favorite). If the kids don't like history, then many places in Ireland might be boring for them..there is a lot of history there. The only time we do the pubs are if we are hungry, and my son's rehearsal diner, and the kids went in with us for that. We didn't go to anything, except the book of kells, and a few inexpensive castles where we had to pay to get in besides the private tours outside of Dublin. I guess the cost in Dublin or anywhere, will depend on what they want to see. Mostly we did the HOHO with the kids, in Dublin, as well as a lot of walking, and then the private tours, which meet at the train station, and then have buses at the other end, and then some of us took the train to Cork, and spent a few days there and did some private touring, both with a car (someone who lived there drove) and again, regular tour companies.
We filled most of a B & B for my son's wedding, and the cost was very inexpensive compared to a hotel. Of course depending on the rate of exchange, it can be an expensive or cheap trip..it's been everywhere from $1.10 to $1.60 per for exchange when we've been there.
If you do get a car, don't plan on filling it with as many people it will sit, and a lot of luggage. The cars are small (although you can rent a larger car, but then the driving is more difficult). Be sure to figure in your gas prices also when deciding to drive or private tours.