Is there a plug-in/widget that exists that would do this for me?
You don’t need a plugin do this. Use WordPress’s feeds. That’s how you get the content out of your site.
Getting the content into the external site is a different matter. WP plugins/widgets only work inside of WP, not outside it.
If you’re handy with PHP, google “magpie rss” and use that to customize how the feed displays on your external site. If you’re not, check out feedburner’s “feed flare” service.