I think it is okay to say "hey mom is happy to talk to you again when you can talk calmly again with me. So I can understand you. Until then you stay here in your room." And leave the crying girl in her room. And at least you are not in the same room as her. My daughter eventually got better about it. The key is probably, first making sure she is getting quality time with you, and second is giving her attention after she calms down. It will probably take a while. I lived through the experience! I am praying for you!
Oh, I am so sorry. You must feel so exhausted. You are gathering all your strength to take care of your daughter and all you get is crying and resistance. I can feel it in your cry! I had a mom friend like that. She had four year old daughter and 12 year old son. She would actually give up on battles with her 4 year old and the little girl got a taste of it. It could be that she learned that she gets what she wants by crying or some kind of attention seeking behavior. Anyway, strong willed child is a blessing, but without discipline it is difficult to control! I would say maybe adopting stronger consequences. Such as spanking. If you are against it, maybe time out. And keep telling her that her attitude is not acceptable and she would not get your attention until she calms down and be a nice person again. I sent my daughter to her room when she had an attitude and told her to stay there until you can be a civil person again. And please seek help from your families and friends!