One piece of advice, if I may. The cursing. It is not very Trek. Yes, on rare occassion in TNG, we hear a curse word (like Data, saying, 'Oh, shit' in Generations
). McCoy cursed little more frequently (mainly in the movies) and there was some in DS9 and VOY.
But never in such profusion and in such explicit comments. For example: “Oh go fuck yourself!” Carol retorted, and Dara pushed her into the turbolift.
She says this to the Captain. The Captain who has previously said: “EJECT THE GOD DAMN WARPCORE BEFORE IT KILLS US!” Alvin’s eyes widen.
It doesn't fit. Neither the story or the universe.
Now, I would suggest you seek some advice: because it doesn't take 5.3 minutes to from Earth to Bajor; it takes weeks or months. Starfleet Captains don't go around telling their own volunteer
crew what a piece of crap starship they've got.
In way, I think this story could work: if you were writing it as a parody on Trek. But you need to take a long hard look and rethink some things.