Multiple Serial Devices

I'm not very experienced with serial port communication and am trying to connect an OLED display and a bluetooth interface to a Mino Pro using 2 analog multiplexers. I'm using the standard arduino serial libraries - HardwareSerial.h I think.

I can get each device to work fine individually but as soon as the bluetooth connects to the the PC the OLED display doesn't work properly anymore. Also, the bluetooth device only works at 115200 bps while the OLED runs at 9600. Can I handle this by setting the correct baudrate immediately before or after picking the address on the multiplexer? This isn't the main problem though as even if I only call Serial.begin(9600), communicate with the display and switch back to the bluetooth address, the OLED display fails right after the bluetooth turns on.

Could the problem be the multiplexer I'm using and if so is there a more appropriate device for this problem?

Sorry, it wouldn't let me add links on the first post. OLED display ( Bluetooth ( Multiplexer (