Rewatching the Promening, and Khan really DID want Uzi to have a good time. He genuinely thought N had hurt her in Heartbeat, and I mean she says it herself she showed emotional vulnerability to him for a second, and Uzi doesn't do that. Everyone by now knows Uzi, especially at that point in time, would only show that level of open emotion so clearly when she's under extreme duress or very much alone with the people she trusts. And she openly hugged him the second she saw him after thinking she'd just watched him die, in front of others.
This isn't a small "whoops" moment, or even a small moment at all- it's a combination of YEARS worth of multiple things repeating day after day, and Khan, though he really doesn't understand her at all and doesn't know what she needs, or know how to give her what she needs, IS trying.
He thinks she's well loved and popular, when she isn't. He's enraged to hear her teacher call her damaged, he's actually really quick to call her too smart for his class (which is genuinely true, making her Sick As Hell Railgun (that's not actually a Railgun) requires a lot more than a high school math problem to figure out blueprints for and actually build!) and stands up for her when she isn't there to hear it.
Honestly the disconnect between Uzi and Khan probably began at Nori's death. Not too hard to figure out, I mean having to mercy kill your wife you clearly love deeply from a slower and even more painful death would mess a guy up. And Uzi looks and acts so much like Nori it's insane.
But I don't think Khan was ever intentionally bad to her. Certainly neglectful, of course, I won't ever deny that. But he wasn't physically abusive or purposely emotionally abusive. He's a dumbass as a parent. He knows he fucked up raising her later in the series, even admits to it himself— "Despite me, maybe." as a response to Doll saying he raised a good kid.
He does figure out he messed up bad by trying to force her to go to prom (given the whole uhh... Doll murder spree thing) and does try to help after Doll attacks Uzi. He's proud of her too, during her speech. He may not think N is good enough to date Uzi, but he stops trying to make her avoid him and instead moves to encouraging her to have friends, almost over correcting the entire opposite into clearly overbearing, having finally figured out that she doesn't have anyone outside of literally N and later V.
Khan WANTS Uzi to be happy! He just hasn't figured out exactly HOW to help her do that.
I mean, he clearly doesn't Get It. He doesn't understand what's going on and knows he wouldn't really be as helpful as N and V would be in Cabin Fever, in Home he's just trying to bring a "sleepover dad" vibe which isn't welcomed because uh Uzi is currently fighting for their memories and possibly lives, and in Absolute End he does try to help!! He rebuilds Uzi's Sick As Hell Railgun, plus he slams a door down on Cyn saving N's core from getting eaten! Casual reminder about that tidbit of information!
He genuinely loves Uzi but is so bad at showing it no matter what he tries, that it just kinda ends up hurting her. I mean, even in the music video??? Khan (and Nori) don't trust that N is good for her even after everything. And Uzi is annoyed by it, then later has part of a ceiling dropped on top of her because N is too anxious about not being good enough that he fails to focus on the fight- THREE TIMES! Honestly if V wasn't there, Uzi could've been hurt way worse than mild disorientation.
But Uzi does kinda show him when he's doing something right instead of making it worse. Which will help them figure out their relationship in the future. It's a mess, but it's clearly getting better.