It's great that you have so much planning time. For many of us, the planning is close to half the fun. I encourage you to visit your local library and borrow guide books for the cities/countries you hope to visit. Start making lists of things you think you'd like to do in each one. Ask yourself how many days that might require in each city (it will probably vary quite a bit). Don't forget to allow time to get from sight to sight, to relax a bit and to eat.
The user-friendly Deutsche Bahn website is great for exploring how long it will take to travel from city to city by train, though you'll have to look elsewhere to see fares.
Skyscanner is a good source for info on budget flights within Europe. Although any flights you'd take for your proposed itinerary would be relatively short, don't forget you'll probably need to leave your hotel close to 3 hours before departure time to allow for security procedures at the airport, and it may take an hour or more after you land before you're at your hotel. (On your arrival day at the beginning of your trip you'll need more time on both ends of the flight.) So even a short flight is likely to take about 5 hours, and it can be longer.
Every time you change hotels, you're going to lose at least half a day of sightseeing time, so if you're planning to spend 3 nights somewhere, you'll really only have 2 full days to see that city plus a few hours on your arrival day.
Research on sightseeing possibilities is really important to help you understand how much time your family (not me, not other posters here, not Rick Steves) will want to spend in each place.
Also keep in mind that many (I think most) people step off overnight flights both jetlagged and severely sleep-deprived. The first (arrival) day isn't much of a sightseeing day for most of us. The last day is basically just for getting to the airport and flying home. So you need to look at how many nights you are prepared to spend in Europe. Subtracting 1 from that number will tell you how many full, non-jetlagged (one hopes) days you will have--until you start spending half a day moving from place to place, that is. Looked at this way, most people's "14-day" trips turn in to 12-day trips, less however many half-days get lost during relocations. It is far better to be realistic from the beginning rather than trying to shoehorn four days' worth of sightseeing in to 2-1/2 days (or 1-1/2) after you've bought your airline tickets and booked hotels.
You interests cover a wide geographical area which is going to see you losing a lot of time on trains, buses or planes. You would benefit greatly from adding more days to this trip.