How to integrate a JS fiddle?

You’re passing true as the $in_footer argument to wp_register_script(), but my_custom_js() is loading in the header. So doubleScroll is loading after the custom js.

I would put my_custom_js() in a separate javascript file so you can control the dependencies.

Create my_custom_js.js in the same place you have the double scroll script:

jQuery(document).ready(function($) {
    $("#double-scroll").doubleScroll();
}

Then in your functions.php use:

function dsb_adding_scripts() {
    wp_enqueue_script(
        'doubleScroll',
        get_template_directory_uri().'/js/jquery.doubleScroll.js',
        array('jquery')
    );

    wp_enqueue_script(
        'my_custom_js',
        get_template_directory_uri().'/js/my_custom_js.js', 
        array('jquery', 'doubleScroll')
    );
}

add_action('wp_enqueue_scripts', 'dsb_adding_scripts');