Here's a sentence that will make Star Trek II sound like a soap opera: David Marcus is Kirk's son…but he doesn't know it.
But don't let that sentence put you off: Star Trek II is much more of a space opera than a soap opera. Marcus is around, in part, as a way of showing that the adventures of the Enterprise aren't going to be stopping just because Kirk has retired to some space Florida to play space shuffleboard.
Marcus is also a doctor like his mother, and is helping her on the Genesis Project. In that sense, he's superfluous to the actual plot…though he does make a great living representation of all the things Kirk has missed out on. He's clearly been up to some impressive things while his dad was out cruising for space chicks.
There's some resentment there too, presumably because Kirk hurt his mother. Even though Marcus doesn't know that Kirk's his dad, he's heard enough from mom to know that he's kind of a louse.
DAVID: Remember that overgrown Boy Scout you used to hang around with? That's exactly the kind of man...
CAROL: Listen, kiddo, Jim Kirk was many things, but he was never a Boy Scout!
That continues into their first encounter, where David basically comes at Kirk with a knife.
DAVID: Mother! He killed everybody we left behind.
CAROL: Oh, of course he didn't. David, you're just making this harder.
Oof. That's evidence of some serious daddy issues. Kirk's got a lot to make up to his son.
But there's a silver lining to this dark nebula cloud: David—and specifically David's resentment—is part of what helps Kirk change and grow: to acknowledge the mistakes he's made and to endeavor to be a better man. Because of that, he earns David's forgiveness and acceptance, which in turn helps him accept the loss of Spock more easily.
DAVID: You knew enough to tell Saavik that how we face death is at least as important as how we face life.
KIRK: Just words.
DAVID: But good words. That's where ideas begin. Maybe you should listen to them. I was wrong about you and I'm sorry.
KIRK: Is that what you came here to say?
DAVID: Mainly... And also that I'm... proud... very proud... to be your son.
Aw, shucks. Group hugs all around.