honestly.. I would cut out one destination. I know , you are thinking but "we have up to three weeks".. well , lets cut that down. First off.. you leave one day from States and arrive in Europe the next day. That day you are pretty beat so arrival day most folks aren't up and running at full speed yet .
Then , every time you move you are spending minimally a half day.. likely more in the move. Even a short move.. like say London to Paris.. its only 2.5 hours by Eurostar. But.. you have to check out of London hotel and get to train station, arriving about an hour before.. so lets assume 1.5 hours from leaving hotel to getting on the train.. plus the 2.5 hours , that's four hours, now you have to get from train station in Paris to your hotel there.. so you are looking at about 4.5 hours for the fastest transfer.. ( which is train as once you start flying, like you would to Ireland, you have to add airport commuting time and the longer wait you have to be at airports before you fly )
So really , if you cut it down to three moves and three places it would be much much better, especially since aren't an experienced traveller and will have kiddos along .
Ps how old are kids?
Also.. how many kids. If you have three it changes things again ( I have three and Europe is not family of 5 friendly.. lol )
All the places you have picked.. there is so much to see.