M.C.
It takes time....lots of time. Your daughter needs to grow up. I agree with what Dawn wrote to you...it's very good advice. Counseling will definitely help your family with this tough situation.
I can sympathize with you as I let my daughter go at 12 years old to live with her father and that was 6 years ago. I see my daughter every few months, but now that she is almost 18, we talk alot more.
My advice to you is to NOT let her back into your home. She made a decision to move out, let her live with it. I can almost guarantee 100% that with whoever she lives with, that person(s) life will not be easy either. My ex and I became much better co-parents when he realized that living with my daughter was challenging.
Focus right now on your family situation. You have enough on your plate with your little kids. Leave the drama with your daughter for her dad. As your daughter gets older, she will come around. It may take time, but it will happen.
In the meantime, when you speak with your estranged daughter, tell her how much you love her and give her your support. Encourage her to excel and succeed at your ex's house. If she gets into a fight with her dad and wants to come back to your house...DO NOT let her. Support your ex and encourage them to work things out. She will learn consequences for her decisions. At the same time, stay away from her. I know that may sound cold, but sometimes you have to practice tough love. Try not to stoop to her level by fighting with her. She wants that...she wants to get a rise out of you. She is angry and hateful. She cannot control her emotions. Time will help her heal and mature.
You need to be a strong mother here. It's easy to stoop to her level, but don't go there. She needs to learn that her behaviors will not disrupt your household.
Remember, always tell her that you love her and support her. You have to love from far away at this point.
Hang in there. Raising children isn't always easy:)