In the Post-Vulgate Cycle and Sir Thomas Malory's Le Morte d'Arthur, it is Morgan le Fay who becomes the wife of King Urien and mother of Ywain (and Malory adds this information).
Thomas Malory's Morte d'Arthur names the first daughter Margawse, the second Elayne and the third Morgan le Fay with no mention of Morgan's illegitimacy.