Parentheses set off extra information. The sentence must still be complete if you lift the parentheses out. Do not put a comma next to a parenthesis unless the comma would belong there even without the extra words. Punctuation overall is in ACT punctuation rules.
The deletion test
The retake (her third) was in October. Remove the middle and the sentence still works. That is the same extra-information test as commas and dashes, in essential and nonessential clauses. Dashes are louder. Parentheses are quieter. Do not mix one dash with one parenthesis.
Punctuation around the pair
A period belongs after the closing parenthesis when the extra words sit inside a larger sentence. If the whole sentence is inside parentheses, the period sits inside too. Quotes around a short phrase are a different mark, in quotation marks. Dash pairs are in dashes on ACT English.
The bottom line
Lift the parentheses. If the sentence breaks, the extra words were not extra. If it holds, keep the pair and leave stray commas off.
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