Q: iPhoto tells me I'm not connected to internet

The error message can be misleading. It can also occur, if Photos cannot render the PDF of your book.

Have you tried to create a preview of the book, to check, if it can be rendered?  try to create a preview as described here:   Preview a print project in Photos, iPhoto, or Aperture to avoid issues - Apple Support

If Photos cannot create the preview, check the page that is causing the problem.

Some software may be intercepting your connection to the Apple Print Products Store.

Do you have an antivirus software installed or a firewall, that could intercept the connection to the store Then try to disable it temporarily and try again to order.

It that does not help, try to boot your Mac in Safe Mode and then order the book in Safe mode.  See this help page:   Mac OS X: Starting up in Safe Mode