I thought that it was a great episode, I love the look on Duras's face when the Earth starships show up or when the photonic torpedoes hit him for the first time, not getting the hint must be a dominant gene in that family. Tripp's loss and his mental state should make for some interesting episodes.
As far as the special team from the "military" goes, it makes sense, if you're going into a potential combat zone, take some specialists in mayhem.
As far as a chain of command goes, they are always under the captains command, unit commander may be equivalent to a commander (major or captain). They could be a separate team or augment the away teams, like Archer said, extra muscle.
BTW, the bridge of Duras's ship took a big hit, but he could still be alive, if Klingon ships have really good survival supplies and systems.
The Earth Starfleet ships were not NX class, one looked like the aft shot in the intro, and one looked a little like a wedge hull, almost like a Texas-class CL from SFB. But they sure meant business, I guess after an attack on Earth, they were looking for some butts to kick and Duras just happened to be handy.
So I give this one a ten.
"Retreat?! Hell, we just got here!", annonymous American Marine, WWI
"Gravity is a harsh mistress....", The Tick