Wrap text around shortcode

Without seeing your show_sticky_posts, show_lastest_posts, show_lastest_missions,show_all_posts_from_categories i can guess that the shortcode content is always before the post content beacuse this functions are echoing/outputing the result and a shortcode should return content instead so you can try using output buffer of PHP like this:

function show_posts_handler( $atts, $content=null, $code="" ) {
    //code 4 displaying 
    extract( shortcode_atts( array(
        'sticky' => 'false',
        'latest' => 'false',
        'missions' => 'false',
        'count' => '0',
    ), $atts ) );
    ob_start();
    if($sticky != 'false'){
        show_sticky_posts();
    } else if($latest != 'false'){
        show_lastest_posts($count);
    }else if($missions != 'false'){
        show_lastest_missions($count);
    }else{
        show_all_posts_from_categories();
    }
    $output_string = ob_get_contents();
    ob_end_clean();
    return $output_string;
}

add_shortcode( 'show_posts', 'show_posts_handler' );