I think you're bouncing around too much. It's three different currencies, four different languages, and with the exception of Florence, all fairly intense places. And all very dense, in terms of sight seeing. One way to slow this down is to go with four nights in Rome with a side trip to Antica Ostia, then to Florence by train for three nights with maybe a day trip to Siena. Then to Lake Como for a couple nights to unwind.
Then, if you want to take your kids to a concentration camp, fly from Milan to Vienna for 3 nights, with a day at Mauthausen.
If you are set on Prague, fly there instead. I think the synagogues of the Jewish ghetto and the graveyard are maybe a better representation of both the history of Jews in Central Europe and the extermination of six million of them. The Pinkas synagogue alone is devastating. There is much else to do in Prague, like the relatively light Museum of Communism. ;-) (really, there's a lightheartedness to that museum that kind of helps with the terribleness of daily existence under the communists for 40+ years)
Alternatively, the Anne Frank House in Amsterdam is probably the least horrifying way to show your children the horrors visited on Jews in the Second World War. As I write this, the memories of these sites returns to me and I have great sadness in my heart. Yeah, Amsterdam is probably the best. And then you can move to a less emotionally heavy site, like the Our Lord in the Attic church. :-) Amsterdam is lovely, uses the Euro, and is completely different from Italy.
Then either night train or fly to Paris or London for your last 3. I see the appeal of doing London now, given the state of their currency and the possible outcomes of their vote to leave, however Paris is still Euro and is wonderful.