Alex knew better是主句，虽然很短，更多深意要看下文才知道。

sensing短语是状语，我们可以理解为对主句进行补充说明就行。本分词短语的语序被打乱了，sense的宾语为that从句，宾语被后置了，即

sensing that I was sneaking a touch of the stubble that had begun to sprout near his ears.

One school night this month I sidled up to Alexander, my 15-year-old son, and stroked his cheek in a manner I hoped would seem casual. Alex knew better, sensing my touch, which lingered just a moment too long, that I was sneaking a touch of the stubble that had begun to sprout near his ears.

1. sensing by my touch：我认为，sense 是及物动词，没有不及物用法。by 多余，属于 typo，应去掉。这样 sensing my touch 是动宾关系的现在分词短语。逻辑主语是 Alex。

2. which lingered just a moment too long，是 touch 的非限制性定语从句，说明“触摸”的时间有点太长了。

3. sensing my touch, which lingered just a moment too long：现在分词短语包括定语从句在内，作“方式状语”，说明 knew better 的方式。