The first thing we need to know is how much money do you have to spend?
Next what are the two rooms, and what is the proximity to each other? For example, is this a lounge and a adjoining Kitchen? If so then separate rooms or open floorplan? Or, a lounge and remote bedroom? Or a bedroom and adjoining bathroom? These details matter.
Next what is your most common music source? Radio? TV? Turntable? CD Player? Computer? Etc...?
You want to both Broadcast music, meaning the same music in each room. BUT you also want the ability to have each room individually select their own source of music. That complicates things. Complicating things even more, is the desire for independent volume controls. If you can accept controls that ONLY turn the music DOWN, that is not that hard to do.
For independent selection in each room, you want computer wired/wireless systems that can pull music off a central computer.
But for Broadcast, that is a single source serving many rooms, you need a wired system like the TEAC, though there are better, but then tend to be pretty expensive. You can buy two amps for less than most Multi-Channel Distribution amps. Also, while you are considering a wired system, consider the proximity of the room and how hard it might (or might not) be to run wires between the locations.
Answer my question, and if you can give us a better or more expanded description of what you would like to do. Budget is very important. If you have a starvation budget, then we must go the minimalist route of one amp, with speakers in two locations, and some L-Pads in the second room to turn the volume down.
The system as you describe it seems a bit difficult to accomplish.
Steve/bluewizard