You can simply start OBS 2 times, however you should not make any configuration changes in the duplicate session, because in case both instances write to the same configuration files, they can get damaged or changes can get overwritten by the other instance.
So first run OBS with only 1 instance and prepare all scenes. Then start it another time and switch to the scene you prepared for recording OBS itself. No changes to any configuration, just start recording and minimize this OBS. Now use your first running instance and show what you want to record. Here you can switch and change scenes and sources and configuration as you like.
To be completely on the safe side, you need both instances completely separated. One regular install and one portable install would work, but this is of course more work.