That's a lot of moving around. Be honest with yourself - how good are you and your kids at being ready on time and staying together. Keep in mind that you can only go as fast as the slowest one in your group, whichever one that is at any given time. Is it hard to get out of bed or out of the shower in the morning? How many bathrooms will you have among you? How fast can everyone pack their things. Does anyone dawdle at breakfast or at shop windows? Is everyone going to wash their own clothes by hand at night? Or are you going to need to spend time at a laundromat (or pay for laundry service)? To me, your itinerary looks too fast for a couple, let alone a group of 6 which includes kids. A couple of things strike me as expecially problematic with your itinerary, aside from too many stops. The fastest train trip I found from Krakow to Prague was 7 hours - and that's just the time on the train. Salzburg is well west of Cesky Krumlov, Vienna is east. It's a 2.5 hour train ride from one to the next, so not a day trip. That means one night in one and two in the other - and one more hotel change. Keep in mind that each time you move, you have to pack, check out, get to the train station (with enough lead time for traffic delays and finding your train), then get from the train station to your hotel, check in and drop your luggage. So you lose half a day or more every time you move. Thus, 3 nights in a town gives you 2 days of sightseeing. 2 nights equals 1 day.
With 15 nights, I'd limit the trip to 4 cities. Given that trains in Poland are not high-speed and that is your "outlier", I'd skip Poland. Fly into Prague, out of Budapest. Stop for a night in Cesky Krumlov, then choose Salzburg for 3N before Vienna or maybe Brno for 3N before Budapest. Or choose Berlin as your starting point, then Prague/CK/Vienna/Budapest
