Circa 970 NE Taringail Damodred marries Tigraine, the Daughter-Heir of Andor, and fathers a son Galad. (TEotW,Ch34)
After the disappearance of Tigraine and the Succession, Morgase marries Taringail to solidify her claim on the throne. She has two children by him, Gawyn and Elayne. (TEotW,Ch34)
LoC,Ch16 - Lady Dyelin tells Rand the story of Tigraine disappearing leaving behind her husband, Taringail, and her infant son, Galad. Rand realizes this as the story of Shaiel, his true mother.
ToM,Ch21 - Morgase is stunned to learn that -Lord Gaebril- was actually Rahvin. She thinks how she was used by men like Taringail and Valda.
ToM,Ch44 - Morgase learned from Taringail that marriage is dangerous so she never made Thom or Bryne her official consort. Gaebril reinforced the danger.