OP I haven't really read the whole thread. However I see you are still unsure.
All I can say is that my own recovery from anorexia was based on plain, harsh restrictions. There was no pandering to my eating disorder. It was you don't gain weight, you can't have your phone. You don't gain weight, you're not allowed anywhere unsupervised.
That's purely anecdotal, though, but from experience of my friends with anorexia, you can't give much free reign as the anorexia is so manipulative. You budge a little, your daughter will take a lot.
I know she's only 15. But she will act manipulatively as she is ill.
If she's relapsed many times, it sounds like you need to try a new approach. Everyone is different. For me it was firm boundaries (and I was 19- my parents stopped all financial support, i.e., if I didn't remain above a certain weight.) The focus was get me to gain weight, then focus on mental recovery after. Often the mental recovery can't begin until physical restoration is complete.
If it were me, my main goal would be making 100% sure she doesn't lose anymore weight. Concentrate on physical health first.
As for your other daughter- you both need a break.
I would go, take other DD and leave your DD with the eating disorder with suitable carers.
Someone with an eating disorder needs to realise that their main aim is recovering. This is why some anorexics are pulled out of school- education, social life, anything else is not as important as recovery.
Your DD needs to realise that. There's no room for manipulation, her only option is getting better and recovering and she needs to realise the consequences of not adhering and committing to her recovery.
So if it means leaving her behind as you originally said and going with other DD, then IMO you must do this.
You need to be so firm. Not because she's a bad person, but because if you don't stand up to her eating disorder and confront it, it will never go away.
She has no reason to recover right now. She probably doesn't see it. From my own experience, a lot of anorexia recovery is about removing freedom and making the individual earn it back.
It sounds harsh. And mean. But anorexia kills and is a very dangerous illness. So in reality it's not really a harsh approach.
I had weekly counselling sessions and got asked to put on weight. I didn't.
Then my phone got taken away, my freedom, internet access, car, money, etc... and suddenly I had a reason to cooperate.
I didn't want to get better for myself, so the only way to get me to recover AT FIRST was to remove the few good things I enjoyed. Then eventually I realised I wanted to get better and gradually I got my freedom back.
Anorexia is a tough and controlling disease. Hence, treatment is often rigorous and controlling.
You have to take the control of the individual.
Again, this is purely anecdotal. This is my experience and the experience of the anorexics I know. Your approach may be different and that's entirely fine. There is more than one treatment option.