I agree, Fanny knows how use emotion as a means to an end. But I think -my impression- that she has a bad temper that makes her easily shout and cry and throw things -as some adaptations show-. As "easily" as a gentlewoman could do it in the protected circle of her home without the world knowing.

So I think she choses to let her anger run free, that are her "agonies of sensibility". She does it purposely, she indulges in her anger, not doing anything to sound sensible or stop her anger, knowing she makes the situation so unbearable to her very civilized home that John and everybody under her is made to obbey her wishes.