Display title of child pages in shortcode

May I suggest you provide details as to the exact problem, and what the results are of your example code?

Also, it seems like you are saying that the pages you want to get the titles of are siblings of the parent, which is the home page, so in fact, they are not children at all (An interesting plot for a TV drama, perhaps).

In any case, instead of using the title for your ID, I would suggest using the slug (post_name) instead:

$current_id = get_the_id();
$post = get_post($current_id);
$post->post_name;

Using the title might results in spaces in your ID, which could result in an array of IDs, not just one.