There was another book my father had bought for me when I was a girl-- A picture book about the Trojan War, it reenacted the lives of the Ancient Greeks fighting in Troy

The "a girl-- A picture book..." is bugging me. Is the punctuation correct?

No, it's not, and there's a problem with the comma after "War" too. This would be better:

There was another book my father had bought for me when I was a girl. It was a picture book about the Trojan War in which I learned about the lives of the Ancient Greeks fighting in Troy.

OR

There was another book my father had bought for me when I was a girl -- a picture book about the Trojan War. It reenacted the lives of the Ancient Greeks fighting in Troy.
[although, honestly, I can't figure out how a book could reenact anything!]

Yes, I like the second one. And I will try to find a better word for reenact.

The word "depict" would work, as would most of its synonyms:

To present a lifelike image of; delineate, describe, express, image, limn, picture, portray, render, represent, show.
http://www.answers.com/depict

portrayed perhaps? but depict sounds good thank you!

You're very welcome. =)

The punctuation in the phrase "a girl-- A picture book..." is not correct. It seems that there is a double dash (--) which is causing confusion. The correct punctuation should be "a girl, a picture book..." to indicate that the girl is the subject and the picture book is being described.