Here is my idea. I have a PS3 in my living room. My bedroom is about 60 feet from my living room, but I don't have line of sight.

If I buy an HDMI splitter and run an HDMI cable from my PS3 to the bedroom, I could play my PS3 on the bedroom TV or in the living room.

The only obstacle I face is the effective distance of the controller. Is there a way to extend that range? Maybe a bluetooth signal repeater? Do those even exist?

i dont think that is possible

The Maximum range of your controller is 33ft (standard range on bluetooth devices) I am not aware of a booster/repeater for Bluetooth. You do not need line of site for Bluetooth.

The controller should reach but waste alot of battery power from far distances. what you can do is buy one of those phone chargers like the razor ones that fit the ps3 controller then if there is a plugin next to were you sit plug in your ps3 controller to the wall so it doesnt run out of battery life.