As long as you pick a date at least 3 days in advance and not too far in advance (90 days?), the Bahn query page should show you some (Dauer-Spezial, Europa-Special) of the discounted fares for that route. If you input a round trip, it will also show you SparPreis discounted fares.
For these "Bahn specials" you can purchase them now, while at home, and print them out on your home printer.
In addition to the discounted fares of the Bahn, which include at least one leg by express train (ICE/IC/EC), there are also regional offers by each Land for about €30 for five people. You probably can't even put fuel in a car for that. Read about them on my webpage. There is also the €37 Schoenes-Wochenende-Ticket for weekend travel by regional train all across Germany and the Quer-durchs-Land-Ticket for regional train travel after 9 AM on workdays, €34 for first traveler, €5 for each additional traveler.
Before thinking about renting a car in Germany, I have spent 16 weeks traveling there, mostly in small towns, all by public transportation, saving about 2/3 in the process. You absolutely don't need a car in Germany. When looking at rental cars, don't look at the cost of a compact. With five people AND their luggage, you will need a much larger, more expensive car.
In Austria, many small towns have regional rail service. An Einfach-Raus ticket would cover your entire family (up to 5) on regional trains all across Austria for only €28 for a day. In addition to rail service, Austria has an extensive network of Post Buses.
In august, I went from Salzburg to Bad Ischl via Mondsee and St. Gilgen, then from Bad Ischl to Hallstatt-Lahn, all by bus. Total cost, one adult, traveling alone, was about €17.