Back when we were big into eBay we used a program called or by Blackthorne and had it networked in our warehouse. Pickers could pull up orders, shippers could enter tracking and customer support could pull up a sale at any time to check its status.
I'm not sure if they're still around but worth a Google.
best is to use magento which is owned by ebay. it will sync most functionalities with its auction site. Ideal for dropshippers IMO