I will be picking up my College Soph after studying abroad. After Prague we are makin our way through Florence to Rome by train. We have only 2 weeks.
1) suggestions on what trains etc to use and how to access them?
2) Any "must sees" Should we go Through Budapast or skip right to Austria?
You might want to start planning your trip by reading Rick Steves' travel books. He goes over trains specifically.
Prague to Florence is a difficult itinerary to plan via train. And budget European air carriers don't fly that route. And from Budapest into Italy is just about as difficult.
You can easily get from Prague to Rome by inexpensive flights, however. You could then double back to Florence in a couple of hours via a fast train. Italian trains are very inexpensive if you buy your tickets ahead of time.
So what you want is a 2-week itinerary through several cities as you make your way down, to Rome, right? You will of course take into consideration which cities your daughter has already visited on her weekends. Budapest is certainly a worthwhile destination but is not on the most direct path. You can easily fill two weeks in two countries. In addition to the big, famous cities, give yourselves a different perspective by including some smaller towns. For instance, see Rick's itinerary priorities for Italy and pick out those that most easily fit your path and timing, e.g., the first 10 days on the list.