I m getting the slug and id of one of the my-category children.
Not sure how to grab slugs and ids from all children.
$incat = get_category_by_slug("my-category");
foreach((get_the_category()) as $inchild):
if (cat_is_ancestor_of($incat, $inchild)):
$my_category_name = strtolower( str_replace(" ", "-", $inchild->slug) );
$my_category_id = $inchild->cat_ID;
endif;
endforeach;
You can use
get_categories('child_of=X')
;
where 'X' is your parent category name..
It will return an array that can be manipulated through foreach.
For more info you can checkout - http://codex.wordpress.org/Function_Reference/get_categories