Theodoric designated his grandson Atalaric as successor. As he was ten when his grandfather died, Atalaric's mother Amalasunta became regent.

Amalasunta was very Romanized according to the contemporary writer Procopius (who was also her magister officiorum). Her pro-Romao-Greek influence on young Atalaric caused a rift with her court, which got so heated it resulted in the execution of three leading nobles.

The chronicles aren't very reliable; Gregory of Tours, who was writing a generation later, held that Amalasunta wanted to marry her vassal Theodad, the Duke of Tuscia, to strengthen her rule as part of a wider strategy to spread Arianism in Italy; an altogether unconvincing argument from the venomously anti-Arian Gregory seeing as Amalasunta was very Romanized. However, Procopius presents the equally unconvincing thesis that Amalasunta was plotting to murder Theodora and elope with Justinian in Costantinople, where she would bring with her the Ravennese treasure.

In any case, when young Atalaric died in 534 Amalasunta married Theodad, who was proclaimed king. Justinian, who had an agreement to prop up Amalasunta should her vassals revolt evidently thought that Theodad was not part of the agreement, and resolved to remove them both.

In all, it's a rather convoluted period of Italian history, and Norwich probably doesn't go into detail because it's altogether unnecessary to understand his narrative about Venice.