Yeah, Carol was definitely more pragmatic. There's nothing in TWOK which precludes the possibility she met Kirk when she was a Starfleet scientist/weapons expert.
The whole nature of Genesis has massive moral implications, which she didn't seem too concerned about. She wanted to create new life on a cosmic scale, and seemed to have a bit of a chip on her shoulder about it ("can I cook, or can't I?").
It would have been interesting to keep her around in the next film, where she would effectively have been the Robert Oppenheimer of the Star Trek universe, having created a superweapon and becoming the destroyer of worlds.
David was young and reckless in using illegal material to make his bomb, presumably because he loved him Mum and wanted her life's work to be a success. But she must have known what was going on too. Maybe he was covering for her when he confessed to Saavik?
Either way, they screwed up, and hopefully after the Genesis incident, she faced the appropriate malpractice lawsuit from the families of her dead team.