They rebel by not testing their blood sugar and skipping their insulin (for example, not taking insulin is a great way to lose weight as long as you don't mind death).
Testing for ketones is pretty much completely irrelevant in preventing DKA; essentially, ketone test strips tell you if high BG is the result of having a bottle of Lucozade without insulin (no ketones) or a dangerous chain reaction caused by complete lack of insulin known as DKA (high ketones).
To prevent DKA, you need to keep blood glucose at acceptable levels.
I'd imagine that DKA can cause problems in school do to kids dying, missing school due to being stuck in hostipal intensive care units a lot and so on.
If your child has DKA you need to get them to hospital A&E immediately. If all your worried about is other kids smelling that your child is deathly ill then, frankly, you should contact social services and tell them you are unfit to care for children.