Is it the same behavior when you put the shortcodes in a post (rather than using do_shortcode)?
I don’t know how to see that on your site so I don’t know what you mean by it doesn’t load? You get a blank map? Or no map?
What tab plugin are you using?
I think the problem is that the tabs plugin must itself call do_shortcode() on its content, otherwise it won’t process the inside shortcodes. When I search on Google it seems a lot of people have this problem, for example:
I’m not sure it would work, but maybe you could first explode the map shortcode, then put the result in the tabs? That way they wouldn’t be nested any more:
$tab1 = do_shortcode("[mashup]");
$tab2 = do_shortcode("[mashup]");
echo do_shortcode("[tab name='tab1']$tab1[/tab1]");