[EDIT] A sheltered American teen, kidnapped by a Bangkok crime lord, is groomed first as his protégé, then as his bride — but when she discovers he was her late mother’s secret lover, she uses his methods to destroy him and seize his empire.

Clarification: my response applies to the "... she turns his brutal methods against him to seize his empire."

Better of the two, IMHO. And at 23 words in length, a quick and easy read.

Or this:

When a naive American teen is kidnapped by a Bangkok crime lord, she must use his brutal methods to destroy him and seize his empire.

Hmmm...The protagonist of the story is the girl, so it's important (to me, at least) that she be the focus of the logline. Here's a more simplified version:

When a naive American teen is kidnapped by a Bangkok crime lord, she turns his brutal methods against him to seize his empire.

Sorry, but [to mangle more metaphors] it seems to me this version of the logline is rather busy; it juggles so many balls in the air, it is difficult for a me to get a clear picture of the plot in ONE READING.

Empasis on ONE READING: Studio suits are very busy, have short attention spans and in the age of the internet have so many distractions, so many excuses to pass on your project. Your logline has only got one chance, 5-10 seconds, to make a strong first impression, to immediately grab and a studio executive's attention, stimulate interest.

[To tell you the truth, at the moment, I'm more curious about the character and story line of the drug lord. After all, he is the one who provides the inciting incident, sets the plot in motion. Not saying you should rework the plot to make him the protagonist. It's your story. But writing a logline for the nemesis/antagonist can be useful in clarifying and strengthening the protagonist 's character and plot line.

After all, every credible villain believes he's the hero of the story.]

FWIW

I greatly appreciate your attention to and insights into this logline!

She is not so much timid as naïve -- ie, not fully formed yet, inexperienced, though with an incipient toughness. How’s this:

When a naive American teen is kidnapped by a Bangkok crime lord and groomed to be his bride, she discovers he was her mother’s secret lover…and uses his ruthless methods to destroy him and seize his empire.