My DD1 had anorexia, DD2 is 2 years younger than DD1. You already know what a terrible illness it is, and how it affects everyone at home, and my heart goes out to you. Just know that it is possible to get through this, we have and many do. But I understand just how bloody terrifying it is, and how much one doesn't want to rock the family boat (more than has happened already) because one has had enough of all the temper, the rows and the threats.
I'd say 2 things: the illness will use what it can to confirm that it is in charge. It loves a row and a chance to manipulate and control. Your DSD2 will find excuses not to eat, and to self-harm, whatever you do. That doesn't mean you should accede to demands, because (as I have learnt, but it was a hard lesson) actually, the more you accede, the more demands there are. The illness has to learn that there are boundaries and they will be enforced. If she doesn't eat, she will be in-patient for longer, or go back to in-patient services.
Second, I remember before my DD went in the first time, not understanding, truly, that there was a safety net in the form of in-patient treatment. You know this safety net is there and so you can rely on it: I know it's not what anyone wants, but she has to be kept safe, and it means that, if she doesn't eat, there will be appropriate consequences. Eating, or not, is her choice.
I remember the desperation I felt when my DD was so ill, and the effects of her illness affected our family dynamics then and, years later, now. If you''d find it helpful I'm happy for you to PM me