This book takes too many liberties when it comes to the mythology. 
Clytemnestra is said to be the eldest of Leda’s four children, Castor and Pollux are five years older than Helen, and Helen is the youngest. She also states Helen is the only descendant of Leda’s encounter with Zeus in the form of a swan. 
However, in the myths, Leda laid two eggs, one contained Castor and Pollux, while Clytemnestra and Helen came from the other. While I understand parentage is debated because Leda has relations with both Zeus and her husband, Tyndareus, on the same night, the children were all born the same: from eggs. 

Honestly, I couldn’t look past this enough to continue. Mostly because these basic things we learn in the first few chapters will have quite the influence later.