I'd be surprised if the total air cost to FAI was that much more than just to ANC, but I'm sure it could be variable depending on specific dates, lower 48 origin points, stopovers if any, etc.

I don't know that the train would be the best solution for surface transport, however. It's a really long ride, and IMO pretty boring for much of the route, and 3 kids could be bouncing around by the time you're there. A car might be a more cost-effective alternative, plus it would allow you to stop in Talkeetna or Denali Park en route, or take interesting side roads, etc. Also I think there are more scenery options from a car than from the train.

But it would depend on the overall itinerary. A car would allow a circle trip - Anchorage - (Denali) - Fairbanks - Valdez - (ferry) - Whittier - Anchorage - while the train only goes on the same tracks back. One-way car rentals are very costly in Alaska however (car rental is expensive, period) so if an openjaw itinerary is anticipated - XXX-ANC//FAI-XXX - then the train might be cheaper.