My thoughts, I would have had the other pilot working the radios. Notifying Approach on the situation and whatnot. Declare an emergency with them if you deem necessary. If you're at a non-towered airport (which it sounds like you were) listen to both and flip the transmitter switch back and forth. Make your calls to unicom and also you're listening to whatever controlling agency you're with.

Any time I've had an issue that required a diversion or an immediate return (including a pax getting sick) ATC was more than helpful and pretty much helped me with whatever I needed. When you dropped off the radar they were probably thinking the worst. They don't like that feeling either.

I'd suggest filing a NASA report on this one just to help cover.