I read the Kinglsey after having read the Hawthorne books. I have the D’Aulaire, but haven’t had time to read those. I am currently finishing up the book “Gods and Heroes: An Introduction to Greek Mythology” by R. E. Francillon.
The Kingsley tells the same stories as the Tanglewood books, albeit in a different tone and slightly different details. The Francillon book has been refreshing in all the Greek mythology books that I have been reading (for myself) in that it is about some of the lesser known stories (although it tells each of Hercules adventures as a seperate chapter) and includes some of the minor gods and other creatures.
If your dd has read the Tanglewood books recently, she may enjoy the D’Aulaire or the Francillon book more.