I'm sure this seems a rather silly post, but I am thinking outloud..
Is it safe to assume that Kirk and Carol Marcus are not romantically involved in this movie as it appears that he is meeting her for the first time?
And yes Spock appears to be incredibly jealous...nice touch that she sits between them. Is this symbolic of her role in the movie? Does she indeed come between Kirk and Spock?
Bones looks a little curious or perhaps put off as well...
Thoughts on this anyone....
Perhaps that's why in TWOK, Mr. Spock and Carol's greeting is a bit cold when she beams aboard the Enterprise
That memory crossed my mind, too. At the time I thought it was a less than cordial greeting, even for Spock. I don't recall if Spock Prime even looked her in the eyes when he greeted her in TWOK.
The only people to whom the name "Carol Marcus" means anything is fans, and maybe just the old ones. From what I've read about how the story unfolds, I don't see any reason why she couldn't have been a brand new character (and just give Admirial Marcus the same surname if it's important that she's his daughter).
(Actually, way, way back, didn't Orci or someone say Eve's character was new to canon? Maybe not.)
So why her? I'm overthinking it, and I know this wasn't any of the creators' motivation, but what I find interesting in choosing to make her Carol Marcus is how she represents a contrast between the two universes. In the prime universe, Carol Marcus is a brilliant molecular biologist dedicated to improving and even creating life. In the post-Nero universe, she's a weapons specialist. Leads me to believe that Starfleet and/or the Federation may have had a type of U.S. post-Sputnik campaign to get the best and brightest to go into the defense and security fields in the post-Nero world.