确实是个棘手的问题。【名词+of +名词】含义非常复杂，前后两个名词的关系有十几种之多，失之毫厘，谬之千里。

He was surprised by the triviality of heranxieties. 她对琐碎小事的忧心忡忡使他感到惊讶。

以上是来自《简明英汉词典》的译文，译者们把整个by宾语处理成主语，尽管很显然【她对琐事的】为主语的定语，可是它与后面的中心词【忧心忡忡】似乎又是密不可分的，否则意义就很奇怪，所以说我个人觉得似乎哪部分都不宜分析为主体部分，似乎应分析为同为主体，类似于动名词复合结构的功能。即：

He was surprised by the triviality of heranxieties.

= He was surprised by her anxieties about thetriviality

= He was surprised by her being anxious aboutthe triviality.

因此你的第1种译文似乎更接近原意。

He was surprised by the triviality of heranxieties. 他惊讶于她的对小事的忧虑。