I would not recommend building any content system feature that needs to be in a specific location. Content system plugins are meant for users to be able to place in various places on the page so that is working against the grain and will only confuse users.
Maybe you just need to implement a UserControl instead of a SiteModule, then you could just put the user control inside divLeft in layout.master and it will be in the left on all pages. If needed you can add the property AlwaysShowLeftContent="true" on the <portal:StyleSheetCombiner and this will tell the master page to always show the left side even if no content system content is there.
Hope it helps,