I don’t think is the fanciest rig you’ll ever see but it worked!
I just used vMix with its built in text graphic to automate the name and appearances of the guests. There were 6 people for the whole show. They were seeing the Master Video and Audio Output when live but I also created a “waiting room” (“Sala de espera” in the shown image) for them to chat while one of them was doing its conference (that one could not hear people in waiting room). There they could also talk to me there.
It’s a really great feeling to create shortcuts and triggers in vMix. And it consumes much less resources than Wirecast in my testing.
This is the result: