Or this may be something as simple as understanding how sources work in OBS Studio, and how order of source makes a difference (which goes in front of/on top of, the other)
Let's say, for sake of example, that you had
- a full-screen video (Window capture, other camera, whatever),
- and then Picture-in-Picture from your 'real camera'
- add another video/picture source 'fake camera', size and position in same place of 'real camera'. In Source list, have this 'fake' source be above 'real source'
- Now, turn on 'fake' camera and it will display on top of 'real' camera. Turn off display (eye-ish icon in source list) of real camera if needed to reduce processing demands on computer
Is that all you are looking to do?