The ESP8266EX have four PWM outputs:
Name pin GPIO PWMx
-----------------------
MTDI 10 IO12 PWM0
MTDO 13 IO15 PWM1
MTMS 9 IO14 PWM2
GPIO4 16 IO4 PWM3
But more importantly you'll also need to drive your rgb strips with drivers such as the ULN2003, very easy to use and can drive 2 strips of RGB leds with its 7 darlington array ; but depending on how many leds to drive, it is probably a good idea to use one per strip, you to evaluate and dimension.
Now for the software remote part ; an interesting design approach would be to use the MQTT protocol (you have several MQTT clients for arduino for esp8266) that now allows you implement Publisher / Subscriber metaphors in no time.
Typically your audio master could publish simple commands to the slaves or slaves sending states via a slave device id path string like "/rgb/dev1/{state|command}' "255,10,10" where state is used to publish a state (typically the slave embedded device) and command is usuallly what your slave receives by the server (your audio master server).
Then your slave would subscribe and then be notified by a command (thanks to your mqtt client) and parse a very simple string message, then set the corresponding color with the PWM's. Note that now your device can also send states very simply to the mqtt server (could be useful for heartbeat functionality as an example).
Note that your design should also consider non PWM digital outputs to drive these leds as it would still provide you with color combinations (i.e. digital R+G pins on give a BRIGHT yellow ...).
Now suddenly, you have many more options for your MCU choice and simultaneous output with only one MCU.
Finally if you want to use the ESP8266 MCU which I think is a good choice for your design , try the Wemos D1 or lua boards for prototyping, they sell for nothing on ebay and are very compact.
cheap esp8266ex compact boards on ebaycheap 50-pcs ULN2003Mosquitto MQTT implementation. For the audio server part good readings (works on raspberry pi too btw)