Is a marriage contracted without the father's consent valid legally and Islamically, and are the children resulting from this marriage considered illegitimate, especially given that the witnesses were from the wife's family?

Marriage of a woman without a wali (guardian) is invalid according to the majority of scholars, based on the Prophet Muhammad's (peace be upon him) saying: "Any woman who marries without the permission of her guardian, her marriage is invalid." Therefore, what the questioner's parents did is impermissible. However, this invalid marriage has some rulings of a valid marriage, such as inheritance, the occurrence of divorce, and the establishment of lineage. Furthermore, it becomes valid and effective, acquiring all the rulings of a valid marriage, if it is affirmed by a Sharia court that deems it so. Consequently, the questioner is legitimately attributed to his father.