This is weird - you've set $CFG->wwwroot = http://REAL IP:8181/moodle in config.php, but when you type http://REAL IP:8181/moodle into the browser, you get an error saying the site can only be accessed through http://192.168.2.2:8181/moodle.
I wonder where Moodle is getting the http://192.168.2.2:8181/moodle displayed in the error message from. The only thing I can think of is that the value of $CFG->wwwroot is cached, but I doubt that very much. On the off chance that it is, clearing Moodle's cache (not your browser's cache) may help. To clear caches, login/SSH into your server and run this command:
php <MoodleInstallDirectory>/admin/cli/purge_caches.phpSee if that helps.
As Ken has mentioned, you're best off setting up a DNS record for your public IP address ('REAL IP') and changing $CFG->wwwroot to the associated FQDN. That will save you a lot of headaches.
One more thing: your router configuration shows that you're forwarding the router external IP (REAL IP) to 192.168.1.99, and not 192.168.2.2 as shown in your error message. Do you have Moodle installed on both hosts?