Anusha.
Look at Jules’ post again. You have six cities and 7 travel days over the course of just 8 days. In 2018, when we took the train from Prague to Vienna it was a good 4 hours or so, not counting getting to the station in Prague from the hotel or getting from the train station in Vienna to the place where we stayed.
We bussed from Vienna to Zagreb because that was the best way to travel in my estimation; faster than rail at that time and not really a much slower than flying when you consider airports. 5 or 6 hours by bus - again without the time from hotel to bus station at one end and from station to hotel at the other, though that wasn’t much since the bus depots were in town.
Perhaps you have limited desire to truly see or experience any of the cities you are traveling through. It sounds like you are enchanted by the train journey.
Is the same true for the rest of the family? Consider, example, if they want to spend a few hours in the Prague Castle and walk across the Charles Bridge or see how the Czech people survived and ultimately overturned the Habsburgs … and the communists. Prague has a charming museum to a fascinating artist, Mucha, whose works will be familiar to you. What of Prague’s Jewish past, or Kafka, or its food and beer, its music or its “Fred and Ginger” building?
Or, might any in your family wish to see the cathedral in Vienna where Mozart was married, or the world class Kuntshistoriches Museum, or any of the Habsburg palaces or the Vienna Opera? What of its parks or markets? If so, then you need at least three days in Vienna.
8 days with your husband and children in central and Eastern Europe should be a time of your lifetimes. Enjoy it.
LATE NOTE. - I really did not mean to initiate a round of folks saying that you have a bad plan. You have a dream of a great train route. I get that. And you will already be in Berlin for you speaking engagement before your husband and kids join you.
All I meant was to initiate reflection for your family trip before you book it.