Is the intercourse that occurs between a woman divorced with a final, irrevocable divorce (talaq bain) and her ex-husband, after her waiting period has ended and communication has taken place between them, and there is a willingness to reconcile, considered adultery (zina) or a return (raj'a)? And what is the expiation for this act if it is forbidden?

A divorced woman, after her waiting period ('iddah) ends, becomes a stranger to her ex-husband. He does not have the right to take her back (raj'ah) except with a new marriage contract (if the divorce was less than three pronouncements). If it was a triple divorce, he does not have the right to take her back unless she marries another man willingly, he consummates the marriage with her, and then he divorces her or dies, and her 'iddah ends.

If sexual intercourse occurred before the end of the 'iddah in a revocable divorce (less than three pronouncements), then the return (raj'ah) has taken place by virtue of it. However, if it occurred after the end of your 'iddah, then you have committed a grave sin and have fallen into adultery (zina). What is incumbent upon you both is to repent to Allah by abandoning the sin, feeling remorse, resolving not to return to it, and increasing in righteous deeds, while concealing yourselves and observing the limits of Allah.

Your family does not have the right to prevent you from marrying this man or anyone else if he is suitable for you. Otherwise, that would constitute obstruction ('adl), which permits you to refer the matter to the Sharia judge.