Fulfillment logistics and warehouse replenishment are completely separate functions from the ordering process. If you do have a complex ordering system, online rules will only confuse both you and your customers. The business system should publish a product catalog so that Smith Cart can collect orders from customers. How an order is picked, packed and shipped, along with performance metrics have nothing to do ordering.
What you could do is handle the emailed orders and route them to the specific distribution center. As the order is shipped you could update the online status accordingly, possibly automatically. Note that this only works when you have one single DC, it fails horribly when stock is required from multiple vendors or DCs.
Lastly, such systems often cost 10, 100 or even 1,000 times more than Smith Cart.