Your original example doesn't quite make sense then:
[ accordion title="MyTitleText" [sitenameshortcode] ]
If WordPress did allow shortcodes within shortcodes then that would become
[ accordion title="MyTitleText" <em>MySiteName</em>]
...which doesn't make any sense.
This would make more sense:
[ accordion title="MyTitleText [sitenameshortcode]" ]
But again, sadly this is not currently possible with WordPress. If you really wanted to be able to do something technically equivalent to this then you could write a new shortcode, call it
myaccordion for example, which would be used in place of
[accordion]. Its only job would be to replace a specific string,
%sitename% perhaps with the site name, before passing on the content to the function
Then all you've got to do is make sure everyone is using
[myaccordion] in place of
[accordion] and understands they have to use
%sitename% in place of
sitenameshortcode. But you're probably going to find you have to do this for every shortcode on your website to make it viable, which would likely get out of hand fast.