The behavior of the child is most probably some thing the child has witness or learned, The best advice is to find out what up brining the child has had before you were involved, secondly look at things that might have result it in the child's behavior. I don't believe the only reason is jealousy and insecurity, if this was the reason the child would have thrown a tantrum ext but violence is some thing a child has witnessed or learned. My best advice see a psychologist if this problem is not sorted out now, you can have sever problems latter on.
Wow, are those kids jealous! Remove knifes from your house. Give the step-children lots of attention. They feel jealous and maybe there is a reason for it. Usually, they feel that they are not getting enough attention and become resentful. They want the other children out of the way, so they can get attention again. It doesn't work that way as we know, but for children they think it does.