Their appearance followed a massive police hunt after the theft of two rifles and two handguns from the home in Chalfont St Peter, Buckinghamshire.
The 14-year-old was sent to local authority secure accommodation while the older boy was remanded in full custody. They are jointly accused of six offences including the theft of the four guns and 40 rounds of ammunition.
They were also accused of causing criminal damage while in possession of a firearm and with attempted grievous bodily harm against a passing motorist while in possession of a rifle.
The 17-year-old faces a separate firearms charge. A second appearance at High Wycombe Youth Court is scheduled for next week.