It sounds quite a convoluted thing to achieve when you both laptops could surely just join the meeting each ?
OBS can combine image/video sources together in any layout you want. So you could be having your meeting with the other laptop person and use OBS to capture that meeting display. You then combine it with the webcam of your own laptop and lay it out in the format you want. You can then set that combined image in OBS to be a virtual camera source.
Then in Zoom ( or any other video call setup ), you select that OBS virtual camera as the source for your video into the zoom meeting. So your zoom meeting will see the whatever you have combined in OBS.
That being said ... camera sources in windows don't seem to like working for 2 different programs at the same time. For example, if you are using your webcam for your 'laptop meeting', you wouldn't be able to also use that same webcam for your OBS combination. Also, you may need to do the same with the audio feeds as well ( Voicemeeter recommended ).
Are the laptops in the same house ? You might be better using a single machine and a second camera source, and combining them in OBS rather than running 2 meetings.
As an example, here is the lads piano lesson setup during lockdown to show the combinations possible ...
Video:
- Camera source looking top down on keyboard showing hand position
- Camera source facing him to talk to.
- Camera source to the side showing his hand positions
- Music software application which lights up which key is actually being played. (So OBS is capturing the display of a running program)
- All combined in OBS ( bottom right on screen ) ... that is the image the music teacher sees.
Sound:
- Keyboard audio source via USB
- Microphone audio for his voice
- Combined in voicemeeter which feeds into Skype as microphone source.
Its overkill, but the teacher says from her side its very very good.