Are the children from the second marriage of a mother, who married before completing her waiting period (iddah) after her divorce from the father, considered full siblings? Is her second marriage legitimate? Does this entail an expiation?

A divorced woman is not permitted to marry before completing her iddah (waiting period), even if her husband had not approached her for a long time before the divorce. If she marries during her iddah, the marriage is invalid by scholarly consensus, and continuing in it is considered zina (fornication/adultery) if they were aware of the prohibition. In this case, the children are considered children of zina.

If it is established that your mother married your father before her iddah from her first husband concluded, then they must be separated. If they were aware of the prohibition, their cohabitation is zina, and the children are not attributed to the man. If they were ignorant, there is no sin upon them for what has passed, and the children are attributed to the man. However, if one of them was aware while the other was not, the sin falls upon the one who was aware.

If they wish to marry again with a new contract, there is no objection to that according to the Hanafis, Shafi'is, and Ibn Taymiyyah. However, the Malikis hold that she is permanently forbidden to him. These children are your siblings from your mother's side, whether they are attributed to their father or not.