Another way to approach the problem is to use a T-stat with a remote sensor. Some stat's average the sensor temperatures. This one does not.
What you could do is mount two aux sensors with a toggle switch and LED. I think with a little logic and maybe a small relay, you can make the switch in either room similar to a 3-way light switch so that the bedroom switch and other switch can switch the locations. The LED on each sensor would indicate which sensor is used. The one in the BR can be very small.
For fun you can make a 7-day timer do the switching such that the programming occurs automatically. You would just need to keep the clocks in sync. The LED's would tell you which sensor was being used.
You could even mount 1 LED abouve the tstat and dispense with the other nonsense. Your timer could be at the furnace.
Swiching all the wires is not a simple solution because of the compressor protection built into the stat.
I think some communicating stats might allow control from two different locations, but it would not switch sensors automagicly.
So, I do think a 7-day timer with 2 remote sensors and one or two LED indicators.