Welcome to Sound Design.
Your co-host will need to use headphones/earpods, etc to stop your voice interfering with their voice.
You can use a TRRS splitter to combine the microphone and headphone leads. There are plenty around but as you're using a Rode mic they make the SC6 for TRRS inputs or the SC6L for lightning inputs.
No microphone can differentiate between different types of sound, only different frequencies.
Human ears have a brain adapted to picking out one sound amongst others, but microphones cannot do this. Some element of AI processing would need to be done. If you're dealing with a pure sine at one specific frequency, that task might be easier, but there will ...