Student or Learner
Something shifted in the air, and suddenly I felt like I was on very shaky ground. “Can you blame me for not wanting to be a demon? Alice killed people, Cal. So did her daughter, Lucy. She killed her own husband.”
He didn’t react to that, so I added—with way too much venom, even for me—“Bet you didn’t know that when you agreed to be ‘betrothed’ to me, huh? Husband-eviscerating apparently runs in my family.” ??
"Husband-eviscerating" would mean to do that to one's husband.
If something "runs in the family" then it is a trait or a characteristic which can be found in many members of one's family. It might be a physical characteristic (Big noses run in my family) or a personality trait (Sarcasm runs in my family) or a regular occurrence (Marrying and divorcing multiple times runs in my family).
In your paragraph, I assume the speaker is related to both Alice and Lucy, both of whom killed people, in Lucy's case she killed her own husband. The speaker is warning her fiancé that it might be a bit dangerous to be married to her, given the family history!