Goal of this post
This post guides you through the steps for inserting the famous DVWP, which is an exclusive part of SharePoint Designer, in a publishing page of a WCM site.
Problematic overview
As a reminder, when trying to open a publishing page with SharePoint Designer, the following message box appears:

Because we can't open the page in SharePoint Designer, we cannot configure and add the DVWP…
Solution
SharePoint Designer contains a very handy feature for WCM scenarios: " Detach from Page Layout ". This will break the inheritance between the publishing content page and its page layout.
First, start by duplicating the publishing page:

Right click on the copied page and select " Detach from Page Layout ": this will embed the layout in the content page.
We can now open the content page as a standard " collaborative " page, configure and insert our Data View Web Part:

Once you've configured the Web Part, you can export it from the browser interface…

… then re-import it in the SharePoint Web Part Gallery:

You can now open the target content page again, and insert your custom DVWP directly in a Web Part zone.
Tip: we recommend you to keep the duplicated page in the library for further modifications!