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