What is the ruling of Islamic law regarding marital intimacy with one's wife after having sworn an unfulfilled irrevocable divorce, thinking it had not occurred, only to discover later that it had, and then paying the expiation, bearing in mind the existence of two daughters from this marriage, and are they attributed to me?

The lineage of children is attributed to the man if he believes his marriage to be valid, even if the marriage itself is actually invalid, as mentioned by Sheikh Al-Islam Ibn Taymiyyah. As for swearing by divorce without intending to enact it, some scholars are of the opinion that it is an oath which requires an expiation for breaking an oath if it is violated, and divorce does not occur by it.