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The database can be shared between the two sites quite easily, as long as they are on a virtual server and all pointing to the same database and an image directory on one domain. That way you could have 2,3,4,10 or a 100 sites all exactly the same if you wanted. Only problem is that if the server go's down then all your sites are down
I use
3dpixelnet.com which use virtual hosting, so its easy for me to controll all my domain using one control pannel. There cheap too about £17 per year for 60MB Webspace, 2500MB Traffic per month, 1 Domain & 1 MySQL DB.
There is a multi/cross domain hack in development I think, and I know other people have multiple databases sharing certain tables.
The only other thing I can think of is if you set up a cron job or something to download a copy of your database every few hours and transfare it to your other site, but you then risk loosing bits of data, and also the mirrored site wont be any good for posting on as it would get copied over by the new data all the time from the other site. I dont know of anything that would compare them and merge the data between them so that you would get a good mirror.
If you were going to intentionaly shut one domain for a period of time, then all you have to do is keep a copy of your files on your H.D, go into MySQL on your server your going to close, do a dump of your database, upload the files to your other server, go into MySQL on the other server and import the saved database. If the domain name is going to be the same then you shouldnt have to alter any files.