Rusudan was the younger daughter of King Giorgi III of Georgia and of his wife, Burdukhan (Gurandukht). Her elder sister was Tamar, who succeeded their father as ruler of Georgia.
When Andronikos was deposed and killed Manuel was blinded, and may have died as a result; at any rate he disappears from the historical record. It is said that Rusudan fled Constantinople with her sons, taking refuge either in Georgia or in the Pontus.
When the Latins seized Constantinople in 1204, Tamar sent Georgian troops to help Alexios and David to take control of the former Byzantine province of Pontus. Combined with their additional conquests this became the new Empire of Trebizond.
Bibliography
C. Toumanoff, "On the relationship between the founder of the Empire of Trebizond and the Georgian Queen Thamar" in Speculum vol. 15 (1940) pp. 299-312.
Varzos, K. (1984), written at Thessaloniki, Ē genealogia tōn Komnēnōn, especially vol. 2 p. 515 note 24.