We are considering the RailEurope pass that has 4 days during a 2 month period.
Actually such rail pass tends to be rather expensive option in your case since you talking about 'our family', thus more than one passenger. If you are willing to spend a bit more time on road by using slightly slower regional trains (instead of faster InterCity), then the best option for you might be Einfach-Raus Ticket (
http://www.oebb.at/en/Tickets/Groups/Einfach-Raus-Ticket/index.jsp), basically daily family pass valid for the whole Austrian network. It cost only 28 EUR for up to 5 passengers, thus much cheaper than any other pass.
As result, you can travel Vienna-Attnang-Puchheim in less than 4 hours (2 changes); Attnang-Puchheim-Salzburg: between 1:14 and 1:34 with none or only one change; Salzburg-Graz: from 5:17 depending on connections (3 changes); Graz-Vienna: 4:01-4:45 depending on connections (2 changes). So in total for all your train transportation for the whole family (<5 people) you will spend only 28 EUR *4=112 EUR. Maybe it's a bit inconvenient to make multiple changes, but on the contrary you get a good deal on Einfach-Raus Ticket. Plus majority of Austrian regional trains in terms of comfort are almost on the same level as InterCity