How can I make the Book Navigation also show the Summary of the Child Page?
--- Potentially not the best solution -----

I haven't tried this but looking at api.drupal.org I think you should be looking at overriding  template_preprocess_book_navigation the variables processed in this preprocess are used in book-navigation.tpl.php ( u are interested in changing output of $tree which is an unordered list by default) I think you can override the preprocess for book_navigation and use a different callback for $variables['tree'] instead of book_children. Your new callback would be based on book_children but additionally load teaser for those child pages. 

I myself would like to see a better solution for this coz sometimes core design decisions are not what we need and would like to know if there are better solutions other than overriding theme engine and replacing a call to a core function with a custom one ( in this case book_children ) Let me know if you find a better solution or if this works.

Needless to say this will affect output of all book pages where book-navigation.tpl.php is used.

Cheers