A friend I don't want?

There's this girl in my gym cl who used to be mean to me and my friends. she would say rude things to us and sometimes grab or hit us. then, one time during gym a tougher girl came and asked us if she had been hitting us. when we said yes, the tough girl went and was really mean to the other girl. when the girl didn't come to school for a few days, our gym teacher got really mad at us. I tried to tell her that we didn't want the tough girl to hurt or be rude to th girl, but she didn't listen. instead she told me in front of the whole cl that I was a very mean student and I need counseling. I had no idea the tough girl was being mean to the other girl. Our gym teacher told us that it didn't matter idf that girl had hurt us, because her mom was ill (nothing serious) and we should just accept it. Well now, about a year later the girl thinks that we are all best friends. How it really is, is that me and two other girls are best friends and the girl is just tagging along. we dont know how to get rid of her. also, this girl is really annoying, she is rude, she always grabs at us, and she embares us. she is one of the least popular people in the school, and everyone thinks we are wierdos because the think we like this girl. we always feel like we have to invite her to our birthday parties,and can never talk about stuff we did together on weekends when she is around. we never have fun around her. I really need help on how to show her that we are not her friends, and dont want to be.