This was my DD a few years ago, and she was the same age as your DD.
Please feel free to pm me.
Honestly - follow what the specialist tells you. I remember thinking that there was no way on Earth it would work, it was only when I reached the end of my tether, and dug my heels in, and stopped putting up with all her excuses that she started to get better. For many months, I thought the hospital staff were talking rubbish, but with hindsight, me giving into her added to the length of tine it took her to recover.
Here are some examples of things that my DD did to try & avoid eating, which I wish someone had warned me about, because then I would have appreciated that it was all an act:
Pretending to drop food on the floor;
Hiding it under the sofa - for a snack I used to give her a portion of nuts sometimes, & we'd have them watching a film...one time, days later, I found a load of them down the side of the sofa so from then on, she ate then at the table with me facing her & watching her every move;
Pretending that she was feeling sick, and fake wretching so that I would not make her eat in case she was sick. In the end, without any emotion, I used to say - you ARE eating it! If you're sick, so be it!
Basically, try & leave your emotions out of it & try to stay calm. She will probably cry, throw a tantrum, try and make you feel shit...tell you that she feels ill, but I can't emphasise how sticking rigidly to the program works.
Happy to message you anytime.
I wish you & your DD all the very best.