It would have been easier when you would have opened a new topic as this has nothing to do with Mobile vs Desktop...
Anyway, it's a bit hard to know what's going wrong as Geocraft from InkThemes is a premium theme. Best guess (read: most obvious problem) is that Dynamic Widgets gets 'confused' by the theme due to inclusion of several post types within one page or heavily usage of custom queries. In the latter this might be fixed by adding a
wp_reset_query() before the sidebar is called.
Also not sure what you're trying of course... Are you sure you're setting DW rules to the correct widget?