Mother [topic-は] me [to-に] that bad news [object-を] hear readiness [object-を] made-do
覚悟をさせた = 'made (me) prepare / made (me) brace myself.' 覚悟 (かくご) = readiness/resolve/preparedness. The causative させた means she caused me to be ready. 悪い知らせを聞く覚悟 = 'readiness to hear bad news.'