Power & Status - It reinforces security. If she could become untouchable, she wouldn't have to sleep at night with one eye open. At least for the threats she worries about.
Revenge - She is not in a place where she thinks about this now. But perhaps one day, if she finds the strength...
Connections - Maintaining social relationships is something she prides herself on, but her motivation to do so is more self-fulfilling than utilitarian for the other Forks.
Change - She wishes to be an architect of change. She believes the world can be a better place than what she suffered. But this would come after acquiring the power to enact it. She is the type to fund an orphanage. If alignments were a thing, she would be a solid Chaotic Good masquerading as Chaotic Neutral/Evil to "fit in".