Her husband forced her to swear an oath telling the truth concerning some sinshe committed in the past

We put this question to Shaykh ‘Abd-Allaah ibn Jibreen (may Allaah preserve him), who answered as follows:

If she is afraid of negative or harmful consequences, such as divorce or a bad reputation, she can swear that she did not do it, and seek forgiveness and do lots of good deeds.

She does not have to offer any expiation (kafaarah) because this oath has to do with something which is in the past, although it involves telling a lie. The kafaarah is sincere repentance. And Allaah knows best.