Is it permissible to go to a park that has a designated swimming area for women, concealed from men, but plays music throughout, and how can one convince a mother who wishes to go and listens to music of this?

We choose the prohibition of singing accompanied by musical instruments due to what has been established in the Sunnah regarding this. Accordingly, it is not permissible to go to a place where this exists, except to change the evil. Advise your mother with kindness, and if she refuses, then you have fulfilled your duty.