OK. You only need to work on the second one then.
Here's what I think is happening, BTW. The config.core.php files in the second site are still pointing to the other site, so you're running the second site on the first site's core. The fact that there's no config file in the second site tells MODX that it's a new install, but somewhere along the line, it's loading the config.inc.php file from the first site -- which is pointing at the first site's db, which already has stuff in, it so MODX is aborting the install.
Since you're doing a clean install. I would start over and delete all the files in the second site. Then put the files there from the MODX .zip file rather than from the first site.
Then look in the DB of the second site in PhpMyAdmin and see if there are tables there (there shouldn't be). If so, drop them all (leaving the DB there). Be absolutely sure that you're in the right DB when you do this.
Setup should then work on the second site if you have the credentials right.
If you have trouble, you might have to create an empty core/config/config.inc.php file for the second site, but probably not.
The moral is that if you want a clean install of MODX, always use the files from the MODX .zip download rather than those from another site.
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