How to make a widget expand wider than the column width when editing its settings in the admin

This can be set by passing arguments to the $control_options of the parent widget constructor, which is the fourth argument. Here is an example constructor:

class Custom_Widget extends WP_Widget {

    /**
     * Sets up the widgets name etc
     */
    function __construct() {

        $widget_options = array(
                'description' => __( 'Featured Pages Widget.', 'affiliate' )
        );

        $control_options = array(
                'width'  => 750
        );

        parent::__construct(
            'custom_widget', // Base ID
            __( 'Custom Widget', 'text_domain' ), // Name
            $widget_options,
            $control_options
        );
    }