He wanted to show that fate ruled people's lives, and that those who interfered with it did so to their sorrow.
【翻译】他想要表明，命运主宰着人们的生活，而那些干预命运的人反而会让自己感到悲哀。

to one's sorrow  某人感到悲哀；使某人悲哀。在本句作结果状语。即：

those people interfered with fate to their sorrow.
那些人干涉（不顺从、抗争）命运，结果使自己感到悲哀。