I've got both sites up-and-running with separate installations on different domains using the one database. I take your point with memory allocation & I'll see how things go, although it seems fine at the moment.
I found that I had to run /setup/default.aspx on the second site, otherwise there weren't any site files in the /Data/Sites directory on Domain2.
Thanks for your help. It's certainly a learning process & I'm amazed that you have the time to help users out so quickly & so well!