My mother tried to reconcile the two of them.

Literal

Mother [topic-は] those two [object-を] make-up-[causative-させ]-[try-ようとした]

仲直りさせようとした = 'tried to make (them) reconcile.' 仲直り (なかなおり) = reconciliation/making up. させる = causative: the mother is trying to cause the reconciliation. ~ようとした = 'tried to.'