Children of children not appearing in book navigation menu
book_children(), which is used in the preprocessor for the "book_nagivation" theme hook (template_preprocess_book_navigation()) only retrieves the immediate children of the current book item, so you wouldn't expect the default "Book navigation" block provided by the Book module to show all children of the current book item recursively.

If you wanted to modify the behavior of this block in your theme, you could clone the template_preprocess_book_navigation() from book.module, placing the function in the template.php file for your theme and renaming it to yourthemename_preprocess_book_navigation(), and then create and call a modified clone of book_children() that recursively collected all links in the book beneath the passed link.

If the behavior you wanted was to display the standard tree for all interior book pages, but display book's entire outline only when you are viewing main page of the book, you could alter your yourthemename_preprocess_book_navigation() function so that it only calls the "get recursive tree" function when the $book_link doesn't have a parent ($book_link['plid'] == 0), and call book_children() for all other cases.