Dynamicly added/new content:
If you're arguing that this is not a "modal dialog", but instead content created by a trigger element (link or button), then WCAG has a slightly different guide on how to handle the new content.
See this WCAG resource on implementation of "Inserting dynamic content into the Document Object Model immediately following its trigger element"
The reading order in a screen-reader is based on the order of the HTML or XHTML elements in the Document Object Model, as is the default tab order. This technique inserts new content into the DOM immediately following the element that was activated to trigger the script. The triggering element must be a link or a button, and the script must be called from its onclick event. These elements are natively focusable, and their onclick event is device independent. Focus remains on the activated element and the new content, inserted after it, becomes the next thing in both the tab order and screen-reader reading order.
Seems to imply, under the "description" section, that to be WCAG compliant, all you need to do is insert the new DOM immediately following the DOM for the triggering button. This applies more generally to what you are trying to accomplish, and seems to satisfy your business requirements. It even provides information on the tab order and current focus following your immediate click.
Clicking the button adds content to the screen. Focus needs to be shifted to the new content, or screen reading users will be lost. Until the dialog has been closed, the user should not be able to tab outside of the dialog.
See this WCAG resource on dialogs
New HTML content like dialogs should be inserted into the DOM directly after the element that activated it. Focus should be sent to and trapped inside the new dialog. The ESC key should close the dialog. Make sure the X (close) button is keyboard accessible and has a text alternative. When the dialog closes, focus should return to the element that activated it.
I was lead to this resource by a Wiki that is managed by the WCAG working group. The wiki/source can be found here: http://www.w3.org/WAI/GL/wiki/Managing_focus_for_modal_dialogs
There are additional resources available, and some instructions/guides around implementation. If your application isn't a web application, many of the takeaways still apply.