I would have a talk with your BFF and then just totally ignore this other person altogether. Nothing gets to them more than when you act like they don't even exist. If your BFF is really your BFF, she'll do the same.
My 'not really a friend' is being mean to me... She always tells me to shut up, she talks to me like I'm stupid, she never takes me seriously and I think she's stealing my BFF... and when I tell her to stop she tells me to shut up?
That happened to me before, but it all turned out good. First, if it looks like she is trying to steal your BFF, talk to her about it! I did it, and it turns out that she felt the same way! So my advice is talk with your BFF, and if she feels the same way, shut out that other friend! She will only make your life worse, so get her out of it!
This doesn't sound like a very nice situation to be in, but I think there are a few different things that you could do to try and help sort this problem out with your BFF.
Firstly, I would recommend talking to your best friend about this other girl.
You should ask her if she feels the same way that you do about your 'not really friend'. If she really is your best friend then she isn't going to let someone else steal her away from you.
You never know, your best friend might even feel the same way as you, and you can work together to try and remove this other girl from your life.
Getting your BFF back
It might be the case though, that your best friend actually wants to be friends with this other girl. Although it might not be very nice to think about, it is going to happen that your best friend is going to make friends with people that you don't like.
Just make sure that you still get to spend quality time together that is just you and her. Why don't you ask your best friend on a day out, or go round each others houses. This way your 'not really a friend' won't get in the way.
When you really have to be with this other girl, there are two options you can chose from. You could either totally ignore her and focus on having a good time. This would ignore the problem but it wouldn't completely make it go away.
Secondly you could speak to your 'not really friend'. Asking if she has a problem with you, and if she does, maybe it could be resolved.
You might have done something to upset her that you don't even know about, and this could be why she is talking to you like she is.
You never know, all three of you could end up becoming friends.