Well, it seems that you have a variety of choices here:
1) Purchase CityStart ticket from Bohumin/Ostrava to Villach directly, in this case 2nd, 3rd, 4th and 5th passenger will pay only 50% of the fare, children <15 go for free. The only problem here is that you'll need to purchase CityStar at least 3 days before actual travel (
http://www.cd.cz/mezinarodni-cestovani/jizdenka/slevy-evropa/-3886/), so you might need to ask somebody to purchase those in Czech Republic or go on your own. Czech Railways don't give exact price of such CityStar, but our guess, CityStar for 4 adults Bohumin-Villach-Bohumin will cost app. 250-300 euro at max. You can email them and ask to be sure.
2) Czech Railways sell discounted eTickets for the route Praha-Villach and Villach-Praha for EC #172/173 (can be bought online in advance -
https://eshop.cd.cz/international/search_cd-obb.aspx), both for 39 euro per person. You can use those not from Praha, but from Brno or Breclav. EC # 173 departs 16:24/17:02 in Villach 22:35, back from Villach 5:27 in Breclav/Brno - 10:53/11:33
3) You purchase eTickets from Ostrava to Wien for 19 euro (even for "Polonia" EC 103), after simply go by slower regional trains with Einfach-Raus-Ticket (28 euro) - will need two changes from Wien to Villach.
4) Not farther than Bohumin and Ostrava there is Slovak Skalite and Cadca, from there you can get similar CityStar ticket to Austria, but even cheaper. Two children go as one adult, thus you'll need CityStar for 5 adults ZSSK<300km OEBB>400. As a result it will cost app. 220-230 euro for all for Skalite-Villach-Skalite via Bratislava. But such route will require couple changes. CityStar ZSSK-OEBB can be purchased even on the day of travel (
http://www.slovakrail.sk/index.php?id=city-star---zlava-pre-kazdeho)