I noticed that when I do a site:domain.com, sitemap.xml shows up within Google's listings. Should I add something to my robots.txt to prevent the sitemap from showing up in Google?
That's strange. Do you have a link to your site that points to the sitemap.xml? If so remove it. Submitting you xml in the webmaster tools should make it show up in the search results.
In your robots.txt you should add the sitemap link so Googlebots will read it as a sitemap instead of a web page.
It shouldn't be a problem that the sitemap shows in the results when you do a site: search. Hide specific pages that you don't want to turn up in searches, e.g. any backend admin pages, but don't worry about the sitemap itself.
I just took a look at my robots.txt and I do have a reference to my sitemap. What else would cause the sitemap.xml to show up in the index? Sitemap: http://www.domain.com/sitemap.xml