Are you able to measure the voltage? The spec says 3.2 - 5.
Another thing to try - run a heavy gauge of wire from the output of your regulator - both 0V and +5, directly to the supply pins of the MP3 module, with a 0.1uF and a largish electrolytic across the supply by the module.
It seems the module uses 3.3V internally. It is suggested that a 1k resistor in the tx line (when using a serial interface) will reduce noise. I would try that in your trigger line.
On a different note, if you go to the separate power supply, if you share the ground with the existing supply, and only use the new supply for the MP3 module, you won't need to isolate the trigger line.