Is this a localhost problem?

I've tried to research the problem, not sure about the solution.

The problem:

The main website where the store is located is www.mydomain.com
When people click to go to the store main page, it properly goes to: www.mydomain.com/store.
However, once on the store main page when anything is clicked (category, product, etc.) the browser address is now http://mydomain.com/store/...... (it drops the "WWW"). This happens on any level, any page below the main page.
The Problem:

The store works perfectly when accessed anywhere. However, the owners of the store have an internal, small office network. When trying to access their own store when in their office and on their network, they get "page not found" on the pages where the "WWW" has been removed. And even after inserting the "WWW" into the address bar, the page text displays, but not the graphics.

The network engineer says that it is because the store is configured with relative addressing, and that when clicking on links while in the store, the "WWW" should be in every address.

How is this problem fixed. The people who own the store cannot properly get to their own store unless they leave their office and access from another external location. /Dan