I don’t think the problem is access to functions, the problem is the admin panels are not widget friendly. Using get_sidebar() may never work because you are trying to load a template into a page that is not template based. You do not need a template to display widgets anyway. You just need to call dynamic_sidebar() with a registered sidebar ID.
If you are widgetizing your own custom admin panel, that should do it. If you are modifying existing admin panels, try one of the methods for adding any other content. Perhaps the Settings API sections or adding a meta box, depending on the target page.