Google isn't very helpful when you don't actually know the name of what you want :P

I'm running XP Pro on multiple computers on a home network. There's basically a 'family' email account as well as personal email accounts, and I'd like to be able to access the family email account on multiple computers but only download it once, if that makes sense.

Here's the current set up: I have my own domain name, with the MX record pointed to Gmail. I am currently fetching my mail from Gmail via POP3, using Thunderbird. We receive a lot of large email attachments in this account (3.5GB last year), so I only want to download them from Gmail once, rather than once per computer. I want to be able to send these emails to multiple copies of Thunderbird on different computers on my network. And also I'd like for the 'sent' folder to be somehow shared between the computers as well, so any email I send from one computer can be read from another. I'd do it by using Portable Thunderbird accessible through a network drive, but then I can only have one copy of Thunderbird open at a time on the network, and that's a pain if I forget to close it on one computer or two people want to check it at once.


Is there anything that does this, and what kind of thing is it called? Can it be done without changing away from Thunderbird or do I have to use a different mail client, as I don't want to have to re-train my parents on another email client? Any FOSS solutions as I'm broke and like to be legal when I can? :)