This topic has never given me any trouble. I simply decide what the
parenthetical material supplies and punctuate accordingly.
In the example given about Hot Cross Buns, the parenthetical material
gives information only about Hot Cross Buns. The sentence is complete
without the parenthetical material, so the period follows the closing
He then formed the Hot Cross Buns (an award-winning group that went
on to win fourteen awards).
This is the same as if the parenthetical material were not included梚t
is extra information.
Another way to do it is to decide whether the material inside the
parentheses is structurally complete梩hat is, is it a complete sentence
on its own? As the Hot Cross Buns sentence is written above, it is not
a complete sentence, so the period belongs after the closing parenthesis.
If, however, you change the wording to "This award-winning group
went on to win fourteen awards," the sentence would be complete.
You would then have two complete sentences, in which case the period
belongs inside the closing parenthesis:
He then formed the Hot Cross Buns. (This award-winning group went
on to win fourteen awards.)