Same blog in 2 different domains, how to?

Probably this is a common topic, but how to install a WP “clone” in another domain? I have an older domain that I’d like to become a clone of my fresh WP install, as I’m finding it easier to manage my image galleries using a blog format, the old site uses plain HTML and is quite boring to update, but this old site is (as it’s older!) already more indexed and linked elsewhere and in Google, so I’d like to just not kill or abandon it but make both work together. Both domains are hosted in the same host, and they can use 2 databases if needed.

This is not a moving process to another domain (which I know how to do, works more or less the same as with for example a PHPBB forum), I’d like to keep an exact working copy on both domains, but all the updating/edit etc. would be made from a single admin interface (could it be the admin of whatever domain I’m connected to at that moment?).

In PHPBB, if I have 2 installations pointing at the same database, using the same table names, they can both work as clones (with a few settings adjustments). Not sure that this is the right way with WP. I read about this in one support page:

WordPress stores two addresses inside the database. These determine where your blog files are, and where the main index is. On a normal install, these addresses are the same.

If in the old domain (let’s call it http://www.domain2.com) I make a new fresh install of WP and set the ‘WP_HOME’ and ‘WP_SITEURL’ of the wp-config.php of this domain to say http://www.domain1.com for WP_HOME and http://www.domain2.com for WP_SITEURL will it work? The config of domain1.com will keep its default domain1.com and domain1.com for both entries.

Of course a very easy solution would be just to make the index of http://www.domain2.com to be redirected to http://www.domain1.com, but this is not what I want.