I'm not clear one xactly what the setup is. To me it reads as:
You have a bluetooth "transmitter" module, an audio module and two bluetooth speakers.
You tested the (bluetooth) speakers using your phone, and sound plays out of both speakers.
You wish to connect your audio module, to your bluetooth module, to connect to the bluetooth speakers, to play sound.
Are your bluetooth speakers "one unit", as in, on bluetooth device, with two speakers attached, or are they two seperate bluetooth speakers, meaning that the tramitter needs two connections?
It could be that the transmitter cannot connect to multiple devices, but just one "sink" that recieves stereo audio. So it can only connect to one speaker at a time.
Note: I am unfamiliar with all the modules you mentioned.
Edit: I noticed the audio output of the MP3 module appears to be differential - it has no common ground it drives both ends of the speaker, rather than have one output a the other ground. So powering these modules from the same power supply, and then connecting the speaker output to GND and the audio input of the BT module will short that amplifiers output, and the other output will be floating at half the power supply voltage. It is designed to drive a speaker, not a single output referenced to ground, at least thats how most 8 pin audio speaker drivers work.