Return only the custom sub-term for custom post type, do not echo term-parent

I’ve made a custom function that retrieves the custom taxonomy term for a list of posts in a query, and echos both the name and the link. Additionally, it also excludes listing a term if I specify the term id (I have a special term, which I don’t want displayed, that I use as a loop hook).

This is achieved by this function

function my_get_the_term_list( $id = 0, $taxonomy, $before="", $sep = '', $after="", $exclude = array() ) {
$terms = get_the_terms( $id, $taxonomy );

if ( is_wp_error( $terms ) )
    return $terms;

if ( empty( $terms ) )
    return false;

foreach ( $terms as $term ) {

    if(!in_array($term->term_id,$exclude)) {
        $link = get_term_link( $term, $taxonomy );
        if ( is_wp_error( $link ) )
            return $link;
        $term_links[] = '<a href="' . $link . '" rel="tag" class="category-link" title="See all stories from '.$terms_as_text.'">' . $term->name . '</a>';
    }
}

$term_links = apply_filters( "term_links-$taxonomy", $term_links );

return $before . join( $sep, $term_links ) . $after;
}

I then display it with this line

<?php echo my_get_the_term_list( $post->ID, 'sports_category',  '', ' ', '', array(3623) ); ?>

All well and good.

Now I am deeper into my site tree and I would like to retrieve the term/s of the current post once again, but now (as I am on the archive page for the term in above explanation) I only want to retrieve the sub-term/s and not display the parent term. I’ve tried modify the above, but I can’t seem to pull things apart.

The examples I’ve seen elsewhere don’t deal with custom terms, additionally I would like to form it into function so I can set some parameters as above.

This is my latest attempt

function my_get_the_children( $id, $taxonomy, $before="", $sep = '', $after="", $exclude = array() ) {
$terms = get_term_children( $id, $taxonomy );

if ( is_wp_error( $terms ) )
    return $terms;

if ( empty( $terms ) )
    return false;

foreach ( $terms as $term ) {

    if(!in_array($term->term_id,$exclude)) {
        $link = get_term_link( $term->name, $taxonomy );
        if ( is_wp_error( $link ) )
            return $link;
        $term_links[] = '<a href="' . $link . '" rel="tag" class="category-link" title="See all stories from '.$terms_as_text.'">' . $term->name . '</a>';
    }
}

$term_links = apply_filters( "term_links-$taxonomy", $term_links );

return $before . join( $sep, $term_links ) . $after;
}

Here’s more of a complete guide based on the $wp_query object:

The Taxonomy

First you might want to know in which taxonomy you are, what its name is and retrieve all its available data from the object.

// Taxonomy name
$taxonomy  = get_query_var( 'taxonomy' );
// Taxonomy object
get_taxonomy( $taxonomy );
// Taxonomy name
get_taxonomy( $taxonomy )->label;

The Taxon/Term

Then you might want to do something with the current taxon/term.

// The current taxon/term slug
$term_slug = get_query_var( 'term' );
// The complete current taxon/term object
$term      = get_term_by( 'slug', $term_slug, $taxonomy );

The Ancestors/Parents

Getting the ancestors/parents offers a lot of possibilities. For example for a breadcrumb trail navigation or post meta data or simply to filter them out of the list of shown taxonomies.

// Ancestors/Parents
$ancestors = get_ancestors( 
     $term->term_id
    ,$taxonomy
);
foreach ( $ancestors as $ancestor )
{
    // The currently looped parents/ancestors object
    $ancestor_obj = get_term( $ancestor, $taxonomy );
    // The currently looped parents/ancestors name
    $ancestor_name = $ancestor_obj->name;

    // Link to the parent/ancestor taxon/term archive
    $ancestor_link = get_term_link( $ancestor, $taxonomy )
}

Is it a hierarchical Taxonomy?

You always will have to distinguish between hierarchical (category like) and flat (post tags like) taxonomies.

// Are we in a hierarchical taxonomy?
if ( is_taxonomy_hierarchical( $taxonomy ) )
{
    // Do stuff
}

Do we have Children, my dear?

Sometimes you’re in the middle of a really deeply nested hierarchical taxonomy. Then it makes sense to handle the children as well.

// Based on the above retrieved data
$children = get_term_children(
     $term->term_id
    ,$taxonomy
);
foreach ( $children as $child )
{
    // The currently looped child object
    $child_obj = get_term( $child, $taxonomy );
    // The currently looped child name
    $child_name = $child_obj->name;

    // Link to the child taxon/term archive
    $child_link = get_term_link( $child, $taxonomy );
}