Your grandaughter does sound like she has a bit more going on than would be typically seen in a child of her age. Although most eight year olds can be difficult at times, her violent acts toward siblings and mom as well as her emotional impulsivity are concerning.
The controlling behaviors, where she shows what appears to be a need to dominate and to have attention over that of her sisters is also a marker that something is occurring that is beyond what is developmentally normal. Plus, the very good and level way she has been approached about her issues, and the very solid attempts to explain to her what is expected...that should have had a greater impact on her behavior than it has.
In an on-line situation it is very difficult to determine what is occurring, although I can say that after working with children for many years her emotional presentation appears to be that of a child with marked traits of oppositional defiant disorder. This issue occurs in some children and although it can be very frightening to witness, the treatment protocols for a child with this problem are well understood. Success in treating this problem is high at her age.
What should you do? I would recommend a formal evaluation by a pediatrician and a referral to a child behavioral specialist. This person will design a customized behavioral plan for the family, and will work to reduce the stress on your daughter and to improve the overall compliance of your grandaughter. This may look very concering, but with the right intervention, this problem can be greatly improved and in most cases, eliminated. Steven