Ever since iCloud integration my phone will use one ID for iTunes and to download apps (my mobile me/iCloud ID), but when asked to update an app, it uses my original apple ID.
Because you purchased them using that ID? Your new ID doesn't get to update apps you purchased under another ID any more than I get to update apps you purchased.
Why did you change IDs for the App Store anyway? There's no reason not to keep your iCloud and App Store IDs separate, and it would avoid the issue you're having.
Because you purchased them using that ID? Your new ID doesn't get to update apps you purchased under another ID any more than I get to update apps you purchased.
Because you purchased them using that ID? Your new ID doesn't get to update apps you purchased under another ID any more than I get to update apps you purchased.
Why did you change IDs for the App Store anyway? There's no reason not to keep your iCloud and App Store IDs separate, and it would avoid the issue you're having.