All DALLAS' sisters-in-law were "crazy". It was a thing. Like shootings and plane crashes.
But Kristin's character motives were clear. As were Lady Jessica's. Hence, they weren't
just crazy -- Kristin was a brazen hussy (a grasping, prostitutional character) while Lady Jessica was a narcissistic grande dame (who had apparently been a grasping prostitutional character in her youth). Both of whom were capable of physical violence. Especially Jessica who, as we would soon learn, was no lady at all.
But we knew, and were told, what drove them.
The problem with Katherine, at least in retrospect, was that the script never informed the viewer as to what drove Katherine -- even as she drove over Bobby in Pam's driveway -- except that she was "in love" with her brother-in-law. There was never even any reference to the fact that Katherine had lost two-thirds of her inheritance to her new half-siblings, Pam and Cliff, and how much resentment that might have engendered.
The only thing that prevented Katherine from being a mere crazy-girl stereotype was that DALLAS was at its creative peak when she was on the show, so we just kind of accepted her and whatever her unspecified goals were (other than her obsession with Bobby). Did Herbert Wentworth diddle her as a child? Did he spoil her, and she therefore just couldn't understand boundaries?
Ray's fatal attraction stalker in Season 11 was equally nebulous in her jealousy mindset, but the series was showing signs of sliding by that point (and she wasn't a sister-in-law, so it didn't really count -- she was just a nutcase floozy he'd picked up in a bar, and who amongst us hasn't done that?)
A lot of Katherine's reasoning could have been delineated even after she'd temporarily died, but it wasn't.
There is some evidence that dark hair dye can seep into your scalp and make you sick, even instigating Non-Hodgkin's Lymphoma. Perhaps that's why she died as the blonde she had once been.
"Why am I so unhappily homicidal??"