We lost our family dog to seizures when my son was just over 3 and deep in the "why" phase. It was not something we'd prepared him for before the occurrence, as it was a gradual decline and reasonably unpredictable death, so my experience is in explaining death after the fact. We ran through all of the thoughts that came to mind as we tried to deal with it and the logistics ourselves - from spiritual to clinical explanations. The one thing he latched onto was a rather abstract last-ditch effort - that our dog had died which meant she no longer lived in her body but from that point forward lived in our hearts. He liked that idea and spent days thinking about it. A few days later I heard him ask his father, "Dad, does Shawnee live in my stomach?" My son is now 5 and has a healthy respect for, but peaceful and not scary understanding of death.
Sorry about your dog - they make good family. Best of luck with your boys.