Dr. Carol Marcus is, to put it mildly, the one who got away.
She's not just one from among the rich and diverse array of space ladeez that Kirk seduced in the original series; she's someone who's really and truly his equal. In another universe—or maybe in an ideal one—they would have ended up together.
But Kirk, space stud that he is, wasn't willing to give up his wandering ways. And Dr. Marcus wasn't prepared to just sit quietly at home and knit while he satisfied his wanderlust (and maybe other lusts, as well).
CAROL: Were we together? Were we going to be? You had your world and I had mine. And I wanted him in mine, not chasing through the universe with his father.
But Dr. Marcus wasn't just about child-rearing. The Genesis Project is her deal, and while it lacks the flash and sizzle of saving the universe in a warp-10 hot rod, the Project looks to solve some very big problems—assuming that marauding space pirates don't get their vengeance-crazed hands on it first.
In other words, she's pretty much 100% awesome.
And this awesomeness makes her unwilling to cut Jim an inch of slack for his reckless ways, and to stress—again—that it's his own fault if his kid hates him.
At the same time, though, she can be gentle. While she and Kirk have a past full of wounds, she still cares about him and is willing to cut him some slack when she feels like he's suffering unnecessarily.
KIRK: And what am I feeling? Old. Worn out.
CAROL: Let me show you something that'll make you feel young as when the world was new.
There's real warmth there, and a shared past that they can both draw from. Considering that her prized creation falls into the hands of a madman, it speaks well of her that she can handle things so adroitly.