Customized Recent Post WP Default Widget issue, need help.

Okay, So I copied the code from the wordpress default widgets and renamed it and added it to my functions php. I wanted to add an image to it which I did and worked. My issue is even though I renamed the widget it also applied it to the default one which I didn’t want. I want to offer the default option which is link only and mine with post image in it. can someone help me out?

Here is my custom-post-type.php code:

<?php 

/**
 * Recent_Posts widget class
 *
 * @since 2.8.0
 */

class jr2_recent_posts_widget extends WP_Widget {

	function __construct() {
		$widget_ops = array('classname' => 'jr2_widget_recent_entries', 'description' => __( "The most recent posts on your site") );
		parent::__construct('recent-posts', __('JR2 Recent Posts'), $widget_ops);
		$this->alt_option_name = 'jr2_widget_recent_entries';

		add_action( 'save_post', array($this, 'flush_widget_cache') );
		add_action( 'deleted_post', array($this, 'flush_widget_cache') );
		add_action( 'switch_theme', array($this, 'flush_widget_cache') );
	}

	function widget($args, $instance) {
		$cache = wp_cache_get('jr2_widget_recent_posts', 'widget');

		if ( !is_array($cache) )
			$cache = array();

		if ( ! isset( $args['widget_id'] ) )
			$args['widget_id'] = $this->id;

		if ( isset( $cache[ $args['widget_id'] ] ) ) {
			echo $cache[ $args['widget_id'] ];
			return;
		}

		ob_start();
		extract($args);

		$title = ( ! empty( $instance['title'] ) ) ? $instance['title'] : __( 'Recent Posts' );
		$title = apply_filters( 'widget_title', $title, $instance, $this->id_base );
		$number = ( ! empty( $instance['number'] ) ) ? absint( $instance['number'] ) : 10;
		if ( ! $number )
 			$number = 10;
		$show_date = isset( $instance['show_date'] ) ? $instance['show_date'] : false;

		$r = new WP_Query( apply_filters( 'jr2_widget_posts_args', array( 'posts_per_page' => $number, 'no_found_rows' => true, 'post_status' => 'publish', 'ignore_sticky_posts' => true ) ) );
		if ($r->have_posts()) :
?>
		<?php echo $before_widget; ?>
		<?php if ( $title ) echo $before_title . $title . $after_title; ?>
		<ul>
		<?php while ( $r->have_posts() ) : $r->the_post(); ?>
			<li>
				<?php if ( has_post_thumbnail() ) { the_post_thumbnail(); } ?>
				<a href="<?php the_permalink() ?>" title="<?php echo esc_attr( get_the_title() ? get_the_title() : get_the_ID() ); ?>"><?php if ( get_the_title() ) the_title(); else the_ID(); ?></a>
				<?php if ( $show_date ) : ?>
				<span class="post-date"><?php echo get_the_date(); ?></span>
			<?php endif; ?>
			</li>
		<?php endwhile; ?>
		</ul>
		<?php echo $after_widget; ?>
<?php
		// Reset the global $the_post as this query will have stomped on it
		wp_reset_postdata();

		endif;

		$cache[$args['widget_id']] = ob_get_flush();
		wp_cache_set('jr2_widget_recent_posts', $cache, 'widget');
	}

	function update( $new_instance, $old_instance ) {
		$instance = $old_instance;
		$instance['title'] = strip_tags($new_instance['title']);
		$instance['number'] = (int) $new_instance['number'];
		$instance['show_date'] = isset( $new_instance['show_date'] ) ? (bool) $new_instance['show_date'] : false;
		$this->flush_widget_cache();

		$alloptions = wp_cache_get( 'alloptions', 'options' );
		if ( isset($alloptions['jr2_widget_recent_entries']) )
			delete_option('jr2_widget_recent_entries');

		return $instance;
	}

	function flush_widget_cache() {
		wp_cache_delete('jr2_widget_recent_posts', 'widget');
	}

	function form( $instance ) {
		$title     = isset( $instance['title'] ) ? esc_attr( $instance['title'] ) : '';
		$number    = isset( $instance['number'] ) ? absint( $instance['number'] ) : 5;
		$show_date = isset( $instance['show_date'] ) ? (bool) $instance['show_date'] : false;
?>
		<p><label for="<?php echo $this->get_field_id( 'title' ); ?>"><?php _e( 'Title:' ); ?></label>
		<input class="widefat" id="<?php echo $this->get_field_id( 'title' ); ?>" name="<?php echo $this->get_field_name( 'title' ); ?>" type="text" value="<?php echo $title; ?>" /></p>

		<p><label for="<?php echo $this->get_field_id( 'number' ); ?>"><?php _e( 'Number of posts to show:' ); ?></label>
		<input id="<?php echo $this->get_field_id( 'number' ); ?>" name="<?php echo $this->get_field_name( 'number' ); ?>" type="text" value="<?php echo $number; ?>" size="3" /></p>

		<p><input class="checkbox" type="checkbox" <?php checked( $show_date ); ?> id="<?php echo $this->get_field_id( 'show_date' ); ?>" name="<?php echo $this->get_field_name( 'show_date' ); ?>" />
		<label for="<?php echo $this->get_field_id( 'show_date' ); ?>"><?php _e( 'Display post date?' ); ?></label></p>
<?php
	}
}

 ?>

In my functions.php file:

/* -- jr2 recent post widget --
----------------------------------------------------------- -- */
require_once( TEMPLATEPATH . '/widgets/custom-post-type.php' );

function jr2_recent_posts_custom_widgets() {
    register_widget( 'jr2_recent_posts_widget' );
}

add_action( 'widgets_init', 'jr2_recent_posts_custom_widgets' );