Let me start by saying that I am familiar only with the original Star Trek episodes so I have no idea how much of this story follows canon and how much of it is strictly AU.
I remember several parts of the story clearly, but not the title, or author, and I have a vague feeling it was incomplete. I also think it was probably a Sentinel fusion, with Kirk and Spock as the S/G pair, but I could be wrong about that. If it was a fusion, I likely read it on Keira Marcos' Rough Trade site, but I've looked through the links posted for past stories on that site and didn't find it. (But, not all authors post links to their work once the site is cleared for a new challenge.)
It begins shortly after the Enterprise has been involved in evacuating a large number of Vulcans from their planet (that was, I think, subsequently destroyed in some sort of attack.) At least one other Federation ship was destroyed, most of that crew perished, in the course of the events that led up to or were involved in the evacuation/rescue.
The Enterprise has been sent back to Earth, (or whatever planet the Academy is on) and Kirk offers the use of his private home to Spock and Spock's parents who are on the Enterprise with them. Kirk's home was previously owned by a Vulcan ambassador and Kirk had never changed many of the aspects that had made it Vulcan-friendly such as having a meditation room, and having Vulcan menu items in the kitchen automation.
Kirk and Spock undergo a hostile Review Board inquiry about the destruction of the other ship. One of the members of the Board lost a close relative (son? grandson? nephew?) who was part of the crew, and wants to blame his death on Kirk and Spock's actions.
One part that I distinctly remember is that Kirk discusses with Spock some gossip Spock had been told about how badly Kirk had ended a relationship with a girl in the past, but Kirk explains he dumped her when she tried to lie about using birth control in order to get "accidentally" pregnant by him, when he'd made it clear he wasn't looking for that type of relationship.
I hope this is enough information that someone recognizes it, and could point me where to find it.