Linking one circuit to two Arduinos
You first need to make a communication between both Arduinos and then you can control RGB led from any Arduino.

For the connection between both the Arduinos, you can make a serial port interface for doing this, you just need softwareserial.h library. Then you just need to connect the RGB LED to one Arduino. Then when you send a command from another Arduino to that one, the Arduino (Connected to RGB LED) can operate the LED according to the command.