Filters on the_content are not applied on a “per shortcode” basis. Post content is passed to the first filter, and then the altered post content is passed to the second filter, and then the content altered by the first two filters is passed to the third, and so on.
You can’t remove a the_content filter, just for your shortcode because the filters aren’t applied that way.
You can sometimes avoid filter issues by manipulating the priority with which you register your filter.
add_filter('the_content', 'twitter_url',1); // run the filter very early
add_filter('the_content', 'twitter_url',100); // run the filter late
In your case, though, the two filters involved– the ones that add twitter_url and do_shortcodes— where not added by you, so it is a bit more complicated and more error prone.
You could have your plugin alter where do_shortcodes runs.
remove_filter('the_content', 'do_shortcode', 11);
add_filter('the_content', 'do_shortcode', 100);
And that might get you around the problem. I have done this on sites I maintain. The concern is that your plugin is altering something registered by the Core. That could potentially cause trouble for themes or other plugins.
The (probably) right answer, which is not possible to construct as you’ve posted dummy code and do not explain exactly what the Twitter plugin does to your code, is to work out what is happening to your shortcode, and why, and find a way to protect that shortcode’s content from within the plugin or from within the shortcode itself. It is possible that a small re-factoring can solve this but that means having the actual code to look at, and not some meaningless filler code.