It's as simple as making another variable. The default example shows music_room = ExtendedMusicRoom(...) -- all you need to do to make another one is music_room2 = ExtendedMusicRoom(...) and use music_room2.add to add songs to it. The default music_room screens all get passed in an ExtendedMusicRoom, so instead of an action like ShowMenu("music_room", mr=music_room) then it's ShowMenu("music_room", mr=music_room2). Or make your own unique screens that directly refer to music_room2 instead of the passed in mr argument so you can style them differently.

I don't really understand what you mean by disabling the music room. Ren'Py's music room base is meant more as an out-of-gameplay unlockable gallery than it is an in-game playback machine, so if you're using it in another way, I'm afraid that's out of the scope of what I can assist with. Basic screen language rules apply here where you can show/hide screens, use variables to enable/disable buttons, and you can always have regular play music/stop music commands in your script.

Hope that helps!