How does a divorced woman atone for not completing her 'iddah due to ignorance and negligence on her part, and does she have to repeat the 'iddah years after the divorce occurred?

One must ascertain the Shar'i ruling before enjoining or forbidding. There is no denouncement when there is a recognized difference of opinion among scholars. Your negligence regarding the 'iddah (waiting period) of divorce and your failure to fulfill the obligations of a woman in 'iddah are reprehensible acts for which you must repent. Nothing is obligatory upon you after the 'iddah period has elapsed. As for observing mourning (ihdad) during the 'iddah, it is obligatory for a woman whose husband has passed away, according to the majority of scholars.