The mother was trying to get through to her son.

Literal

Mother [topic-は] son [to-に] reason-make-listen-[try-ようとしていた]

言い聞かせる is a compound verb: 言う (say) + 聞かせる (causative of 聞く = make listen) = to talk sense into someone. ~ようとしていた = 'was trying to' — the past progressive of the attempt.