Looking at how media buttons operate on the posts page, it’s not going to work while the other is present…
They’re not designed to be on the page twice, and i can’t see any way to modify it to support 2, at least not without several additions all over the place.
Think about it, the uploader is designed to send data to one place, the post page, and specifically that ordinarily only has one place that supports shortcodes (ie. [caption][gallery] and so on).. so there’s never been a case where it would need to support more then one area.
Above approach i mentioned would change where the code gets pasted/inserted, but as i mentioned this then also effects the media buttons that normally placed regular inserts into the content area.
It’s either, or…i’m affraid ..
Unless someone with more knowhow of WP js and jquery can chime in and suggest something more..
If there were a JS script equivalent of add_action/add_filter then i’m sure it would be possible (with the right know how – beyond my capabilities as it stands though).