Influenza most commonly spreads through aerosol means--coughing, sneezing, even just talking. The photo below is well-known:
It can also spread through surface contact--someone sneezes or coughs, covering their mouth and/or nose with a hand, and then leaves a contaminate on a door handle, a sink spigot, or some other such commonly used surface.
Children in schools often prove more susceptible because they are crowded together more than people in a workplace, and they often don't do anything to prevent the kind of aerosol contamination shown in the picture above. Diseases, mild and severe, commonly spread more rapidly in schools than in other venues. I don't know, of course, but I suspect that that explains why your daughter succumbed, but you didn't.