Reading one RF remote and controlling multiple RGB LED strips

I've purchased a RGB LED strip with a RF remote and receiver, but this remote/receiver combo can only controll one strip and I want to place multiple strips in my living room. Also the default RGB programs of the controller s*ck and I want to program them myself. I am an experienced programmer, but I'm quite new to Arduino and hardware.

My plan is to replace the RF receiver/controller with an Arduino to read the RF signal and controll the LED strip. I then want to put an Arduino at every strip in the room and all read the same RF signal.

I want to buy three Arduino's with RF modules, but before buying all this stuff I want to know if it's possible what I want to do. A link to an article or tutorial on this topic would be even more awesome. I bet I'm not the first one in the world who wants to do this...

Edit: this is what the receiver and remote look like: