One of the common misconceptions I hear is that if someone has books published through a publisher that they cannot have a store on their site. While it’s true that exclusive distribution agreements, such as those signed with a publisher, will prevent you from selling your books in your webstore, there’s no reason why you can’t build a webstore to gain all the other benefits while still directing readers to your publisher’s preferred site.
A good eCommerce system will have what’s known as “affiliate” or “external” products. These are products that aren’t sold directly on the site. Instead, the button links directly to the page you choose. This means if your publisher has its own webstore (and it ought to), then you can link there. Or use your Amazon Associates affiliate link and link to your book on Amazon. (You can see this in action here: http://marywinter.com/shop/well-tuned/.)
As you can see from the example link above, this same link works well if you’ve independently published through KDP select/Kindle Unlimited. It’s exclusive arrangement is very similar to that of a publisher where you cannot sell or offer your books elsewhere. Only Amazon can do that. Including your Kindle Unlimited books in your store will bring them to the attention of your website visitors, link directly to your Amazon page, and make sure that you get the sales you’re wanting.
While it is true that some of the benefits of having your own eCommerce site such as more money for each book sale won’t be available to you if you publish through a publisher. It is also true that you don’t have to miss out on the promotional opportunities that having a webstore affords you.