Do you actually live in Austria? Because I've seen comments about family tickets. I only know Switzerland - where your kids under 6yo will travel with you for free and your under 16yo half price.
For older kids there are a lot of discounts, but many of them are only cheap if you use public transport regularly. (eg. rail card family from the ÖBB for 19€ a year, or upper austria regional tickets for school children for 77€ a year, etc.)
One problem is that it's not just train tickets, but you also need tickets for bus/tram/subway, and every city/region has different systems, so for every trip I spend about 15min trying to figure out which tickets to buy.