We are told that Anne prefers playing the piano to dancing. From Chapter 6 Anne, very much preferring the office of musician to a more active post ...

This is hardly her being kept by the Musgroves playing music. It is her volunteering. What part of the text do you see as saying that the Musgroves are keeping her playing? Can you please provide a quote, because I can't recall such an indication?

Anne is also given the opportunity to exhibit like the Musgrove girls. We are told that her performance was little thought of, only out of civility, or to refresh the others, which means that though the Musgroves were incapable of appreciating her skill at the piano, they, out of courtesy, sometimes thought of her performance (and sometimes when the others needed a break too). What is your source that she never has a chance to exhibit?