I thought her "as long as the music plays, we dance" statement was a statement on fate and hopelessness. She feels trapped by circumstances and believes that they will dictate how she acts in the future. In other words, even if she wanted to stop her current course, she can't. And the rest of the world is in the same situation. It was a metaphor for being a victim of circumstance.
She makes several allusions to being trapped or bound by fate, destiny or circumstance during her encounters with Hawke, seeming to recognise them as someone else who's course on the ocean of the world is often dictated by the currents, rather than their hand on the rudder.
Hawke: We don't have much choice.
Flemeth: We never do.
I don't think Flemeth believes events to be set in stone, but merely recognises that certain people are "destined" for certain things, because despite having the choice to do otherwise, it would be contrary to them to do something else when placed in that scenario. Morrigan expresses something similar in Origins, commenting that they do have the choice to leave Ferelden to fall to the Blight, rather than save it. She explains to the indignant Alistair, that even if it is a bad choice, it is a choice nonetheless, even if there seems like only one course available for them to take.
We see this viewpoint in Flemeth's non sequitur to Hawke ("Hurtled in to the chaos, you fight... and the world will shake before you") that has her recognise that when placed into a difficult situation out of their control, they will fight to stay afloat, because that is simply the person they are. Likewise if you pick the dialogue about being tricked, she explains that she could have picked anyone to bring the amulet to Sundermount, but chose Hawke specifically because she knew not everyone would have succeeded.
I think that's probably how Flemeth is able to nudge history in her favour, seeking out particular people and placing them in circumstances that will leave them with few choices, banking on them making the choice that is most in line with her plans. Sort of similar to how Asimov's Psychohistory from the Foundation series works, but Flemeth's methods include predicting individual actions, as large scale events.
For instance, we know that Marethari was in debt to Flemeth and WOT2 implies she sought her out in exchange for some way to get revenge on the Avvar who murdered several of her clan, her husband and mortally wounding Mahariel's father. Given how the Sabrae clan found both an Eluvian, were instrumental in Flemeth's restoration and Merrill became a companion of Hawke, it makes me wonder how much Flemeth manipulated that clan to her own ends. Perhaps the reason they were in the Brecilian forest to run into the Eluvian in the first place was because of her?
*Takes off tin foil hat*