Your subject is the tree. The verb is staring. Are the trees staring? No... Your subject needs to be performing your verb.
It's really that simple.
Staring at a spot in the darkness, the trees swayed to and fro.
I get what the author is trying to say, especially when I read the rest of the paragraph. A man is walking through the woods, spying on a cabin, but I shouldn't have to think about it. The subject should be clear and the verb even clearer. In the sentence above, the subject is the trees. There is no clear subject, really. I assume it's the trees. The action is...staring or swaying, one or the other. More confusion.
He stared at a spot in the darkness and noticed the trees swayed to and fro.
Now your subject is the man and your man is performing the verb. Both are clear.
Deepening the kiss, his hands caressed the bare skin under her skirt.
His hands are the subject. How can they deepen a kiss?
As he deepened the kiss, he caressed the bare skin under her skirt.
Now, HE is the subject and he's deepening the kiss and caressing her. It's more clear.
This often happens when a passive sentence is in use. Watch those passive sentences and make sure your subject is always performing the verb. While you don't want every sentence beginning with HE or SHE, neither do want them all starting with ING words.
Thanks for reading!