Adriana had no way around this, as her parents laid only two options before her. She either nurses Aiden Rockerfeller back to perfect health, just like she met him earlier, or leaves everything in City C and comes back home.
It was not emotional blackmail to use her revenge plan against her, however, Adriana needed to understand the gravity of what she did, and the effect it could have on them all. The Hastings never use their superiority to suppress anyone, and Vicker was not going to destroy his friend's life by turning a blind eye to this.
Adriana's compliance was what surprised everyone around her because they all expected her to put up a strong resistance. However, she did no such thing. It was clear that she had realized she was at fault and was ready to make amends.