There's ballroom dancing to live music in the Wheelhouse Bar. Unfortunately, on MV Golden Princess, the Wheelhouse Bar is much too small to accommodate the number of people who go there and the dance floor is much too small for serious ballroom dancing. If you are serious ballroom dancers, you would be much happier on any of the following ships.
>> MV Sun Princes, MV Dawn Princess, MV Sea Princess, MV Ocean Princess -- both the Wheelhouse Bar and the dance floor are much larger than aboard MV Golden Princess, so there's no trouble finding space.
>> MV Royal Princess -- the Riviera Club is the equivalent spot, with live music for ballroom dancing and, again, both the room and the dance floor are much larger than aboard MV Golden Princess.
I hope that it's not too late to change your booking.
I can't advise regarding either MV Regal Princess, as I have not been aboard either her or her sister.