I tried a similar solution to this problem a few years ago.
I wore a MP3 player and listened directly with an earpiece. My partner listened via a bluetooth link connected to a second output on the MP3. This did not work well because the bluetooth processing introduced a significant delay to the signal heard by my partner. I assume your A2DP streaming will give an almost identical delay for both partners so that should not be a problem.

My solution was to use an analogue radio microphone based link instead of the digital bluetooth. That also allowed our teacher to have the MP3 player while my partner and I both had radio mic receivers. An expensive solution but I happened to have the radio mics already.