I liked this story a lot. Thanks for sharing it! The idea of these three characters trapped in such a poisonous relationship is great. I particularly loved these lines:

Beckett, also, was impossible to get unclothed.
This is a very interesting idea indeed. I cannot imagine Beckett naked and vulnerable. To my mind, he’s always wrapped with layers of expensive clothes.

Beckett called him nothing but Admiral, using the title more like he was calling his well-indulged pet.
Indeed. Beckett can use a title as the ultimate insult.

Unless his lack of reaction had soured the taste of power in Cutler’s mouth.
Great line! Beckett lusts for power so much I wasn’t surprised he was vexed at Norrington’s indifference.

As I said, a great story- will you be writing more? ^_^