She hasn't "chosen" him. Please don't think like that - she needs to feel you both love and care for and want her. Usining language like "choose" is the worst thing you could do for her. She is still your child, still loves, needs and wants you, and by insisting that her loving BOTH parents is a rejection of you, you will damage her. She had to decide to live somewhere and right now, it's with him. But life is long - hell, adolescence feels it at the time - this is just an episode in our lives.
I appreciate that your ex is someone who may be very bad news. But if she is to grow into a stable, happy and healthy adult, that's a conclusion she has to come to without any advice or input from you. Leave the door open always to her, make it clear that you love her, and just stop talking about her father at all. Her relationship with him is none of your business.
You say you are faced with coping with the hurt and rejection by your eldest. I would rather say that your eldest has been forced into a corner and made to choose between Mum and Dad while still a child - how painful must that be?
You haven't and won't lose her if you try to remember that your relationship with her father is totally separate from his relationship with her, and her relationship with you. She has a right to love you both, and see you both, and live with either one of you, without the other casting that as abusive and a rejection.
I do appreciate it must be agony, and agree you should seek counselling. But you can't blame our daughter - she hasn't done anything wrong.