Her behavior shows some classic hallmark of sexual and or other abuse (mental, physical). Children who are overly touchy or craving attention often are acting out what they're not getting at home--namely, affection and proper adult guidance and supervision, or what they are getting--abuse.
Her behavior towards animals and other children is also problematic and might signal domestic or sexual abuse. Either she may be witnessing abuse or experiencing it herself. There's always the chance that she's seeing her mom and mom's spouse/mate engaging in sexual behavior. If that's the case, it's problematic, too. It's one thing to catch mom and dad in the act, but her behavior suggests it's a regular thing, so if mom and her mate are being sexual in front of the children, that's totally inappropriate.
There's also the possibility that she has something physically wrong with her brain--sometimes growths in the brain result in violent or aggressive behavior. Some children with brain tumors even experience suicidal ideation or commit suicide. A CAT scan might provide more answers.
The fact that her mom is not interested in her child being counseled or assessed is a major red flag, imho. If she's aware of the abuse, or engaging in the abuse, she of course will want to hide that fact.
Personally, I would first sit with the girl and question her, in a nonjudgmental way, about her home life. Maybe play a game where she can draw pictures of all the players at home and what they do. You can ask what they do when she does something wrong or is bad, or ask where everyone sleeps, or where mommy and daddy (or other mate) touch her when she's going to bed or how she gets a bath). Some of these questions, if handled properly, can reveal a lot. If you see a lot of very real clear signs of abuse (like she draws people hitting each other, or heads cut off or people touching their private parts), I would call the police and ask about the procedure for reporting to child services. Some child welfare agencies are good; others, like the ones who dealt with the California family whose parents drove their car off a cliff in a murder-suicide, are clearly negligent. They had all the warning signs of abuse and didn't act quickly enough.
If you're going to report your sister, you have to consider the welfare of the child. Are you willing to take her in, or is there another capable, qualified relative who can? Because leaving her to the state or a foster family could prove more problematic, certainly in the short term.
I'm sorry you are experiencing this, and I'm sorry for the little girl. There are a range of odd or wild behaviors that are pretty normal for young kids, but the degree of her maliciousness suggests a more troubling underlying cause, and I hope for everyone's sake that she can get the help she needs right away. Perhaps try talking to your sister again, and give all the reasons for your concern. If she continues to push back, I would take matters into my own hands. Even if your relationship with your sister suffers, you are doing something to protect a child's life and well-being, and that counts for more, imho.
Why are you talking to the little girl about it? Especially if she is the product of abuse? Why not talk to her parents? They'd be the ones to help her. You ARE accusing her. Why be covert? If you think her child is dangerous to yours, it would make sense to be up front about it and discuss the problem maturely. Your only other option is to limit time with that family. Because it is wrong to go to the child and try to 'talk to her' or to judge her without brining her custodial parent into it. When you say you can't point fingers, you actually ARE at the little girl. Seven year olds are rarely evil but a product of other things going on. So, you either have to be upfront about your concerns or stay away. And if you fear for her and think your sister is a part of the problem, call child protective services to investigate. But you can't help the little girl in this way. Even with the best of intentions, it wont' get anywhere. And your sister will view you as problematic if you are going behind her back or thinking all of these things and not talking to HER about it too.
But in general, when I read your first post, it appears you really just don't like her. Feel like you are stuck with the situation so maybe it is best in the long run for all to just back away and limit time spent with them. And if the sister asks you why, then be honest and talk about her daughter's behavior.