The Compound by S.A. Bodeen

Fifteen-year-old twins Eli and Eddy have the best father in the world who also happens to be one of the richest. When the world comes under a radiation attack, their father sends the entire family to an underground compound to protect them from the radiation effects. Unfortunately, Eddy and Grandma don't make it into the compound before the door is sealed. Six years pass with Eli believing his twin brother and grandmother have died in the attack. Little by little, though, Eli realizes his father has not been completely honest with the family about what really happened. When he discovers a laptop that still has an internet connection, Eli is able to reconnect with the outside world. But can he save his family before his father destroys them all?