You do not want your XML sitemap to include duplicate content. In your case, it sounds like that one product exists at multiple URLs, which is the very definition of duplicate content. So, what I'd say is that you want to have the page mywebsite.com/product1 (the canonical version of the URL) in your XML sitemap, then keep the others out of your XML sitemap.
Including all the versions of the URL won't help. Likely, it will just confuse Google and may lead to Google ignoring certain URLs in your XML sitemap. To get the most out of your XML sitemap you don't want Google ignoring any pages from the XML sitemap. In my experience, keeping the XML sitemap clean makes it more useful. That means no error pages, no thin content pages, no redirect pages, and no duplicate content pages.
Also, keep in mind that there is no guarantee Google will follow your XML sitemap. Even if you put in the canonical version and have the rel canonical tag on your pages, Google may still choose to treat another version of the URL as canonical.
Ideally, then, I'd solve the real problem here and just have one version of the product URL on your site (have the versions with the category in the URL redirect to the version of the URL with no category in the URL). That way you don't even have to worry about all the issues duplicate content may cause.