My mother insists that I must not go out after dark.
Literal
Mother [topic-は] dark become-[after-てから] I [subject-が] go-out-[must-not-てはいけない] [quotative-と] insists
暗くなってから = 'after it gets dark.' 言い張る = to insist/persist in saying — 言う + 張る (to stretch/persist). Stronger than 言う alone; implies the mother won't back down.