She mistakenly thought that her period had finished; she did ghusl and had intercourse with her husband, then more blood came
Question

My wife thought she completed her menses (although earlier than normal) and began praying. I then went to her. After the fajr prayer the next day.  She then made ghusl and prayed Dhuhr. Is there any sin on me or my wife, and if so do I have to make kaffarah?
Praise be to Allah.If a woman thinks it most likely that her period has finished, and she sees the signs of tahaarah (being pure, i.e., after the period has ended), so she does ghusl, prays and has intercourse with her husband, then there is no sin on her for having intercourse, because it is an action that is permissible. What is forbidden is to have intercourse at the time of menstruation.  If the menstrual blood comes back, then she is considered to be menstruating and she is not allowed to pray or have intercourse with her husband, because when the menstrual blood is flowing, the rulings attached to it apply. Its signs or features are well known to women, so a woman should not be too hasty in doing ghusl and starting to pray until she sees the white discharge which is the sign of tahaarah (purity), or she is completely dry in the case of one who does not experience the white discharge. Cessation of bleeding alone does not mean that she is now clean, rather she is clean when she sees the sign of tahaarah and when the usual time for her period to end has come.
And Allaah knows best.