That's not too easy.
You can set the email account to "leave messages on server" on both machines, but then you have to go to their webmail to clear that regularly.
When it's set on none of them, like now, it's first-come-first-served: the one that happens to ask first (and maybe it's set to once in 10 minutes independently) gets the message.
When you set it on only ONE, the OTHER PC gets ALL messages and THAT PC only part.
In other words, you've discovered why webmail (gmail, hotmail etc) is so popular by people using more than one PC.
As an alternative, consider the use of "hosted Exchange" as a central place to store your data. That's MS Outlook compatible.
I have a home wireless network for my main PC and a wireless laptop. I like to use Microsoft Office Outlook 2003 for managing my emails. However, when I am on my wireless network my emails only come to one of my computers randomly - sometimes my main PC and sometimes my laptop. Is it possible to change my settings so that emails come to both computers while they are connected to my wireless network?