Unfortunately the fastest public transport option between Prague and Nürnberg is a 3.5 hour bus ride. The shortest train connection is 4.5 hours, and from personal experience this is a very scenic, off the mainlines trip, however the timetable is limited.
Travel between Nürnberg and München or Stuttgart is very easy and comfortable with the fantastic ICE (InterCityExpress) trains running frequently, getting you there in no time. The problem I always seem to have is that my ICE trips are too short - I settle in, start enjoying some food and tap beer (Warsteiner is from the keg on ICE trains) and find that I could happily travel all day but must get off because my stop has already arrived!
All that said, you'll be travelling with small children so a car would provide convenience in terms of carrying the luggage and supplies. However space, movement, activities and relaxation are restricted in a car compared to the train.