From your diagram, it looks like you want to send a radio ping, and an audio ping from one Arduino, and to receive that radio and that audio ping on each of the other Arduinos. If this is correct, here are a few thoughts.
First of all, the low-cost ultrasonic distance modules such as the ones in the PDF file you pointed to, are set up with a fair bit of internal circuitry that allows them to send a burst, wait for the return, and indicate that return on a pin (the same pin on some models).
I haven't tried doing anything like the method I think want to do, which is to send a ping from one module and receive it on another, but I suspect that the receive side of the module will not be enabled, and thus, cannot receive a ping, until it has been enabled by setting the transmit pin to send the ping.
Unfortunately, using individual piezo transducers to build a custom setup is a fairly complex undertaking, requiring a good knowledge of electronics; amplifiers, detection circuitry, etc., though there are several circuits out there. A search on Google Images for "ultrasonic sensor" schematic will yield quite a few.
Perhaps, if you have access to an oscilloscope, you could find some point on the module to wire into that would allow you to either enable the receiver, or to detect a received ping without having to first ping with the transmitter.
Hmmm... just had a thought. Perhaps this might work...
For the transmit: Leave the unit as is.
For the receive: Disable the transmit, perhaps by unsoldering the Tx element
Method:
Transmitting:
Transmit a radio signal
Immediately transmit a ping
Receiving:
On receiving a radio signal, send a ping on a modified sensor (no Tx).
Wait for a return, as you normally would. It will not be an actual return, but a ping from the other unit.
Should work within about 6.6 metres or perhaps further. This is double what the specs for the module are, but the sound only has to travel one way.