That would be option 3 then JJ?
Just to picture it:
Incoming Mail -> Demon -> Gmail IMAP -> 2 clients with Live Mail IMAP -> Gmail IMAP-> Outgoing mail with ***@demon email address
I can't remember the exact trouble I had last time I tried to sync Outlook with Gmail, I just gave up. I just hope it would be as easy as it looks. My parents would be very unlikely to access the gmail part of the process so that may help.
I would be tempted for a belt and braces approach and have gmail forward all mail to a second gmail account.
Something tells me using gmail may ruffle my mum's tinfoil hat.
