If you fancy a bit of an adventure (and a chance to meet a local), consider taking a Bla Bla Car.
Bla Bla Car is a ride sharing service (very popular amongst economical and efficient Germans) who advertise free seats in their cars, as well as their departure time and date, to people who want to get from A to B. Basically you agree to a car share and chip in for the petrol. If often works out much cheaper than the train and faster than the bus, and the driver hopes to break even by picking up a paying passenger.
Granted, with a family of five, it is very unlikely that you'd all be able to travel together, but you could easily split into three plus two.
It is a little unusual, but it could work for you.