Can this women use this photo without permission?

How do you know she does not have permission.

You obviously don't know who took the picture and therefore have no idea whether she has permission to use it or not.

She does NOT need permission from the child or parents (unless they are the copyright holder of the image).

The missing element here is the photographer. If the parents signed a model release for the photographer, it may have given the photographer unlimited rights to use the child's picture, including commercially. If the photographer then sold a license to the author for use of the photo, she then had legal permission and there's nothing the parents can do. If they didn't sign a model release, then the book's publisher is violating the law by using somebody's visage without permission and an agreement for proper remuneration. It's not technically a copyright issue because the photographer as owner of the copyright may have given permission. But for commercial use they also need a model release. So contact the publisher (not the author -- unless the book is self-published). Ask to see proof of permission. If they stonewall you or fail to produce it, contact an attorney and sue everybody.

Regardless of who took the photo, she may not use this image, especially of a minor, on a product such as a book. I smell a very successful law suit here!

The publisher needs photographer's permission; if she didn't take it, it can't be published

I would consult a lawyer but if it is being used commercially I would say that is copy right violation.

you should take permission.