Complex sentence: To avoid the vengeance of the Emperor, she fled with Andronikos to the court of Nur ad-Din, the Sultan of Damascus; but not deeming themselves safe there, they continued their perilous journey through the Caucasus and Anatolia.
Split into simpler sentences: To avoid the vengeance of the Emperor, she fled with Andronikos to the court of Nur ad-Din, the Sultan of Damascus. Feeling unsafe there, they continued their perilous journey through the Caucasus and Anatolia.