How to a build a payphone controlled iPhone?
I doubt an mobile phone would do it.

A GPRS Modem would definitely do the job, if it has microphone speaker terminals.

The key is the microphone and speaker connections.

Not a simple solution, the GPRS modem has a learning curve.  At first glance it appears to be very similar to a regular land line modem, do not be fooled. it is nothing like a regular land line modem.  

I have an old Multitech GPRS modem where the serial cable broke out to a separate phone jack.

Multitech no longer makes it.  I was also buying knock offs of the Multitech out of China with a 20 piece minimum. There may be some of them floating around still.  Ericsson Telecom made an inexpensive unit 

This is NOT the one I have, but the connector is 15 pin video connector not a DB-9 as most GPRS Modems have.





Connector Pin out, notice mic and speaker.



PDF Manual GPRS Modem