The misfortune was so terrible that readers couldn't hold back their tears.

Literal

Misfortune [topic-は] too terribly, readers [topic-は] tears [object-を] suppress thing [subject-が] could-not.

あまりにもひどく = 'so terribly.' 涙を抑えることができなかった = 'couldn't suppress tears.' ~ことができなかった is the past negative potential pattern.