Whoa, mom, please back up a bit and slow this train down. You started out asking about switching her out of advanced classes and into "base" classes then suddenly are saying you "hate her friends and her behavior also" and that "this kid is horrible." I think you started out focused on the academics and suddenly went off into behavioral issues that have clearly built up some emotion for you.
First, please, please don't send her to yet another new school to "fix" this. That only will make her resent you and school profoundly and she would be even likelier to rebel than she already is. Also do not cave in to her desire to be in base curriculum classes -- if she left the previous private school because she was academically bored, it is utterly wrong to let her leave her more advanced and challenging classes now that she is in them and doing well as you note.
Why are most of her friends at the new school kids who are not in her classes at school? If that's the case, where and how is she getting to know them? What is attracting her to them? You really need to explore that some. Are they kids from classes like gym or electives where kids from all kinds of academic classes are mixed together? It's fine and in fact good and healthy for her to have friends who are not necessarily in her advanced academic classes, but if you dislike these specific kids and their influence, I'd start encouraging her to do things with kids from her classes. Do you really know these friends pretty well, or do you just "see" them through her tendency to want only to be with them? They might be OK kids but you resent their taking her away from her activities and influencing her to want to change classes.
Also, why and how did she drop her "lots of extracurricular interests" when she changed schools? Were those activities tied to the old school somehow (after-school clubs at her Catholic school) OR were they not, and she just dropped out?
If the interests and clubs etc. were tied to the old school, of course she had to stop them; you now need to require her to join an activity or club at the new school and I would also tell her she needs one other activity totally unrelated to school ( you want her meeting kids who share her interests, not just kids whom she knows only because they are at the same school.
If she just suddenly dropped things that were not tied to the old private school, that's kind of on your, mom, and you need to acknowledge that; talk to her and present a lot of options and let her choose some things to do that she finds fun. Let her feel she has some real say in what she does but have her do something.
All she does is talk on the phone? Time to limit her phone. My 14-year-old doesn't even have one and when we get her one for high school it's going to be the kind with a limited set of people she can call (yes, it will include certain friends) but no texting and no internet. You may feel you can't go that far, and doing so might make your kid rebel worse, but if she is busy and is doing activities that force her to be phone-free, she won't be on the phone "all" the time, and she will make friends at those activities and be less apt to call her other friends (though that may take time).
It sounds like you and she are not communicating at all, and she may feel she's being controlled while you may feel she's being obtuse about her future and her friendships. It sounds like she's doing a classic middle school dance called "You aren't the boss of me and my friends are more important than you, mom." This is really normal though it can be very painful for the parent. How you handle that pain is really important right now. If you are feeling a lot of anger with her, please see about getting both of you to a family counselor or yourself to a counselor so you can handle your own emotions at what is a tough time for you and for her.
She very likely knows how you feel about her friends and about her. Even if you never used the word "horrible" to her she very likely knows that's how you feel and sometimes that makes a preteen or teen decide she'll act so badly she'll justify your opinion of her. I would try to get away with her on a completely fun trip somewhere, even a day trip or a weekend, with activities she helps plan, so the two of you share some experiences that are positive and you do not bring up school or her friends at all during that time. It is not a fix but a way to get a breather and give her some input on fun. But most of all I'd see a counselor about your own anger (if it's as expressed in the post, maybe you were having a bad moment there!) and would get her involved in activities. Please update us.