C.M.
All of this sounds so normal to me. My daughter (7) goes to public school, although a charter/alternative choice school, but has many of the same things going on. She herself has done/said some mean things in the past that I've heard about and we've talked about. It's all part of learning their place in the world and part of it is learning what they can get away with. (One time she and two of her established friends took a vote on whether or not another child could join their group! She wasn't being mean, really, just insensitive.) We talked about how that might have made the girl feel excluded or hurt and how would she feel.
She has a neighbor who is also her best friend, and occasionally there is conflict where one of them will say or do something to hurt the other (the "I'm not your friend" has come up many times). But I just try and tell them that it's not an acceptable way to express their anger. I try to tell them that friends do disagree or even fight, but that it doesn't mean the end of the relationship and they know that and wouldn't truly want that anyway...they usually agree with me on that.
As far as peer pressure goes, try to focus on what matters. If it's a specific tshirt or shoes, and you don't care, let her dress to fit in. But you could also voice your support when she chooses to do something different (my daughter refuses to wear the school tshirt on spirit day...). If it involves an activity that I feel strongly against, I don't mind telling her that it's not the first or last time she's not going to get to do something, wear something, have something, etc. that someone else does. If appropriate, I will explain my reasons. Do make sure she is very clear about appropriate and safe behavior at school - if she's being asked to do something mean or unsafe, help give her the words to refuse...literally put the words in her mouth. If her cousin is just acting out in her own 6 year old way, you can help them work through it. If she truly is a bad influence, this is a perfect time to start teaching your daughter the way to decline gracefully. After all, there are plenty of "naughty" kids in the world, if it's not her cousin, it will be someone else. Good luck.