Listing categories by ID not alphabetically

I want to list which categories are attached to a post.

I have a parent category and several child categories..

If I select the parent category and a child category and I want to list what categories I’ve attached to a post, how do I list those categories so they are sorted by ID and not alphabetically?

My problem is in my sidebar I have a list of the last 10 posts in the parent category.
However I want the list to include the name of the child category so the list looks like this:

LAST 10 POSTS IN X CATEGORY
—————————
CHILD CATEGORY – POST TITLE
CHILD CATEGORY – POST TITLE
CHILD CATEGORY – POST TITLE
CHILD CATEGORY – POST TITLE
CHILD CATEGORY – POST TITLE

and so on.

My plan was just to use this:

<?php $category = get_the_category();
echo $category[1]->cat_name; ?>

However as it sorts the categories by name, if I have a child category starting with a letter before the parent category it screws up and writes the parent category instead of the child category..

Anybody has a suggestion?
Thanks a lot in advance!