The bus costs 2300 Yen and takes about 2.5 hours... it goes point to point and drops you off in the center of Hirafu village.
The train is not a bullet train, just a "regular" train. The whole journey takes around 3 or more hours, probably closer to 4 after you factor in the additional taxi / bus ride from the station to Hirafu. Bear in mind that the train journey has 2 legs, the express train with fewer stops from the airport to Otaru. At Otaru, you have to switch to a local train that stops at every station along the line. I think I had to wait 40 minutes or so at Otaru when switching trains. I think the train cost about 3000 Yen not including the ride from Kutchan to Hirafu.
One reason why the train would be more cumbersome with small children is that you have to carry all your luggage with you, up and down stairs, and onto the train itself (no separate luggage compartment).
Check out the "JR" (Japan Rail) website for more info and train fares / schedules.