I decided that after my daughter graduates, I'll leave her to do as she pleases.
Literal
Daughter [subject-が] graduated after [topic-は] self [possessive-の] like entrust [nominalizer-こと] [dative-に] decided.
自分の好きに任せる = 'leave [it] to [someone's] liking.' 任せる ('to entrust, to leave to') takes に for the recipient. ~ことにきめる = 'decide to X' (a decisive resolution). Parent making a post-graduation hands-off decision.