The men, aged 23, 24 and 34, all from the Preston area, have been bailed until Friday, March 14.
Four men burst into a house on Tuesday evening and threatened the family before stealing a number of firearms from a safe.
During the robbery at the address in Halfpenny Lane, the woman and her two sons, aged eight and 10, were threatened and tied up with dressing gown cords.
The two children also witnessed their mother being punched in the face.
Officers have been making door-to-door inquires and asking neighbours if they had seen anything suspicious between 3pm and 7pm on Tuesday.
The robbers, who are also believed to have been armed with knives, made off in a white transit van with a number of firearms including a pump action shot-gun, a deer rifle and a foxing rifle as well as ammunition.