The point at issue is not her ability but her personality.
Literal
Problem [to-に] has-become point [topic-は] her [poss-の] ability [not-ではなく] personality [copula-だ].
問題になっている ('has become a problem, is at issue') uses ~ている for a resulting state. ではなく ('not X but') is the conjunctive form of the negative copula, creating a contrastive structure.