。
She hadn't intended to fight with him.
Literal
She [topic-は] he [with-と] fight do intention [contrast-は] there-was-not.
~つもりはない is a stronger negation of intention than ~つもりがない: the contrastive は emphasizes 'as for an intention to do this — there was none.' This phrasing distances the subject from the action. けんかをする is a light-verb construction — けんか ('fight') verbalized by する.