You're right that the second 'they' refers to the parents, but there is a much simpler way to determine it. "Today's generation of children lead a much less active life than their..." The subject is the children, so 'they' refers to the children. "...their parents did when they were young." The subject changes to the children's parents, so the next 'they' is referring to the parents. "Today's generation lead a much less active life than their parents did when they are young." This is not a valid sentence. "Today's generation lead..." - 'Generation' is third person singular, so it should say "Today's generation leads..." "...did when...are..." this changes the tense, and is thus invalid. "...did when...were..." is a consistent tense (and the original sentence). "...do when...are..." is a consistent tense. With corrections: "Today's generation leads a much less active life than their parents do when they are young." This is grammatically correct, but it still doesn't make sense. As for the reasons I stated before, the second 'they' has to refer to the parents. The parents were young in the past and never will be again, so this sentence is invalid. To determine what the 'they' is referring to, you need to know what the subject is at the time (usually the last noun that was mentioned in plural).

Children are already young. It obviously refers to the parents.