What does she do that is mean? It almost sounds as if the fact that she doesn't play with dolls and enjoy tea parties equates with meanness. I was never very "girly" as a child (I still am not). And my daughter is a lot like me. I have two older brothers and no sisters, and had no female cousins younger than me. My daughter likes to "compete" with my son (who is older than her) and plays with him and his friends. She also has friends that are girls, but they actually usually play outside together.. and often involving my son as well. She is JUST getting where she will let me paint her fingernails (she is almost 9 yrs). And she STILL refuses anything pink or flowery looking. Picking an Easter dress was a NIGHTMARE (But we found a nice blue and green polka-dot she was able to live with, lol).
It sounds to me like your daughter is just trying to fit into the family dynamic she has found herself in... the younger sibling to 3 older boys. And frankly, from that perspective, it is very easy to see how she might be trying to physically assert herself to make her own place in the family. Boys tend to "value" physical dominance.. and I bet they ignore her up until she whacks them. I am NOT saying that it is acceptable for her to hit, only that I can see how she might tend that way. Does she get time to play with other little girls without the boys around? She may not play "Barbie" in the traditional way (my daughter used Polly Pockets and Spiderman action figures to play out superhero sequences... not to dress her up and play kissy with a "husband" or shop), but she may play more quietly than the boys would (you won't even HEAR my daughter in her room playing.. even if the toys are waging war, with boys you will hear every "explosion" and "shot" fired, lol).
I have found that even with just one boy and one girl, I sometimes had to tell my daughter that it was okay for her to play dolls or want to play with her hair, etc. She would sometimes act embarrassed to want to do these things. Now that she is a little older, she has more female friends of her own and when she goes on sleepovers, they play board games and Polly's and paint fingernails, etc. She is much more her own person.
As for being "girly" vs. being "mean"... be careful not to compare the two things. They are not opposites. Mean is not being sensitive to how you make others feel, or hitting, or being selfish. You would discipline a boy for the same things. Girly is not the same as being "nice". She doesn't have to be "girly" if she doesn't want to, and you can't make her. You shouldn't make her. You can encourage her and let her try out dolls and dresses and flowers and frilly things, and soft colors, etc.. but if she doesn't like them... welllll, then she doesn't. That could change later. Or not. But it isn't wrong or need to be corrected. Meanness... that is just a discipline matter.