Remember how happy she was back in chapter 1, when Seiichi told her about how he dreamed about the dead cat, but got disappointed he couldn't remember how it died? And in some other dream about the same day, Seiko apologizes to Sei? My guess is it was one of those stray cats everyone in the neighborhood cares about, and Seiko hated it. Either Seiko manipulated Sei into killing it, and Sei got scratched, or she killed it herself, got her hand hurt, and manipulated toddler Sei into hurting his own hand (or she injured his hand herself). Either way, I think Seiko made 3-year-old Sei swear a blood pact with her, to be always together.
Now I'm really curious about the whole "they know we're murderers" thing. There's no way they're blaming a 13 year old for that murder attempt (even after what auntie said). Is she just trying to test him? Or is she talking about their shared "mental condition"? Or it's got something to do with her past (cat and who knows what else)?
And I find it difficult to believe the police are going to give much credit to what Shigeru says, he's brain-damaged. She's getting caught only if she or Sei confess.