In other words, you want to turn the MediaWiki wiki into a live mirror of the Confluence wiki. Correct? Sounds like a nightmare. :)
The opposite, i.e. a live mirror of MediaWiki wikis, is rather easy: you just call action=render
on the desired page (example) or use the appropriate parsing API to get the HTML. The MediaWiki URLs can be made RESTful with $wgActionPaths
. This is the strategy used for instance by the Wordpress plugin Wiki Embed.
Confluence is not that easy to use and its web APIs look quite limited, but you can attempt fetching the HTML of a page. Embedding HTML on individual MediaWiki pages is feasible e.g. with $wgRawHtml (I suppose editing rights are restricted on this wiki). You will need to do this manually for each page because Confluence doesn't have free linking and you won't have an automatic way to map titles to URLs.