Right. Your remote sends out a signal that will turn a tv off that is on and turn a tv on that is off. The remotes recommended above will send out signals that say turn on or turn off. In other words, there are three signals that can control the on/off state of your tv. One tells the tv only to turn on, one tells the tv only to turn off, and one tells the tv to reverse its on/off state.
If you use the signal that says "only off," it will turn your bedroom tv off without turning the other tv on.