Complex sentence: Her paternal grandmother, Irene Palaiologina, was a daughter of Michael VIII Palaiologos and Theodora Doukaina Vatatzina which makes Asanina a member of the extended Imperial family of her time.
Split into simpler sentences: Her paternal grandmother Irene Palaiologina was a daughter of Michael VIII Palaiologos and Theodora Doukaina Vatatzina. Which makes Asanina a member of the extended Imperial family of her time.