Check if a post is in any child category of a parent category

Add the following to your theme’s functions.php:

/**
 * Tests if any of a post's assigned categories are descendants of target categories
 *
 * @param int|array $cats The target categories. Integer ID or array of integer IDs
 * @param int|object $_post The post. Omit to test the current post in the Loop or main query
 * @return bool True if at least 1 of the post's categories is a descendant of any of the target categories
 * @see get_term_by() You can get a category by name or slug, then pass ID to this function
 * @uses get_term_children() Passes $cats
 * @uses in_category() Passes $_post (can be empty)
 * @version 2.7
 * @link http://codex.wordpress.org/Function_Reference/in_category#Testing_if_a_post_is_in_a_descendant_category
 */
if ( ! function_exists( 'post_is_in_descendant_category' ) ) {
    function post_is_in_descendant_category( $cats, $_post = null ) {
        foreach ( (array) $cats as $cat ) {
            // get_term_children() accepts integer ID only
            $descendants = get_term_children( (int) $cat, 'category' );
            if ( $descendants && in_category( $descendants, $_post ) )
                return true;
        }
        return false;
    }
}

Use the function to check the parent category ID, not name or slug. I.e. if the ‘movies’ category ID is 50:

if ( post_is_in_descendant_category( 50 ) ) {
    // do something
}

If you don’t know the ‘movies’ category ID, you could retrieve the ID using get_term_by() and pass it to post_is_in_descendant_category():

$category_to_check = get_term_by( 'name', 'movies', 'category' );

if ( post_is_in_descendant_category( $category_to_check->term_id ) ) {
    // do something
}