You should really work as close as possible with your diabetic team, as dealing with very young diabetics is different to that of an adult, they do run in similar lines, but the approach to Blood glucose control will differ as this is due to it being as you are probably already aware that maintaining blood glucose as a set range is very very difficult...
Your team will be abe to advice you on blood glucose levels ranges to aim for, that should provide a safety net alonside providing protection against long term problems... These ranges are likely to change as your son grows...
As to food, learning and knowing carb content is a very good idea, as to what types of foods he should eat, a normal healthy balanced diet.. Swapping things such as normal jellies to sugar free jellies... Restricting but not totally avoiding such things as ice-cream etc...
As already said, for snacks or fillers, cucumber, carrots, celery, chunks of cheese, slices of meat all help...
Another trick with children, if they become a eater that may not want all there meal, is to inject there insulin after they've eaten so you can adjust accordlly
It might be wise at this stage, to take a look at insulin pumps, and discuss this with the diabetic team, as this is a more flexible method of controlling diabetes in children also having the advantage of avoiding dailly regular injections...
As who's to blame, well no-one except mother nature! I'm the same i come from a very large family indeed but I am the only diabetic of any type!!
It goes without saying, that you and your son have a hard road to travel, but you will do it you will get through the difficult times, there is no reason that your child shouldn't thrive and grown as any other child, the treatments, regimes and understanding are constantly improving all the time...