Currently there doesn't seem to be a way, using the Scripting API, to add page items to other page items. We can do it easily via the UI using Cut and Paste Into.

The obvious place for accessing this existing feature via scripting is the PageItem.move function. It currently accepts a Page, Spread, or Layer. If this method allowed also Rectangle, Oval, etc, we could do this intuitively. It is a glaring shortcoming.

See this forum post for a discussion. There is no solution for this thread.

(Note: invoking menus and polluting the clipboard is a terrible way to do this, and is impossible on Indesign Server anyway.)