The only 2 companies I have heard of that could do something like this are:

1-Airship: they have automated all the processes of dispatching, logistics, customer support, credit analyses, order fulfillment, etc on the backend. In the front end you just built your own e commerce website. It is plug & play and that easy.

2-Indemand. (Tryindemand.com)
They built the order management, inventory system and dispatch on the back of a white label e-commerce site. They are focus on grocery stores so don't know how much it will fit your specific needs.

(Disclosure I know both CEO's and have invested interests

Two great sites are http://www.shopify.com/ or http://www.squarespace.com/. The both have content management systems that are build and managed by the companies, have integrations with Google Analytics and best of all they have the whole billing flow/system taken care of, which for a commerce site is one of the most important things to get right.
They provide base themes or allow you (with a little elbow grease to learn their respective templating languages) to completely control the front end.
If this is for clients you get the added bonus directing them to the Shopify/SquareSpace customer service for more backend technical questions about payments etc.

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