OP it sounds like your DD is on the spectrum too. Just because it doesn't show in the way it did with DD1 doesn't mean to say it's not for DD2.
The restrictive eating, the isolating herself, it's very much a pattern there of autistic teenage girls.
I would break down in front of her. She needs to see you have emotions too and that you can be broken too.
She needs to see the impact of her behaviour on you. You are not your DM and your relationship with your DD is not the same. You are absolutely allowed to make this a little bit about you, some of the time. Not all of the time of course.But some of the time yes. it's important that you show her you're human and you have boundaries too.
Also, do you tell her you love her? Do you share with her the mistakes you've made?
She may also have AFRID which is often linked to ASD and means she finds textures, smells and colours hard in foods and she may have found food difficult all her life. Just allow her to get on with what she can eat and don't judge her harshly for what she can't or won't. Often it's not a choice for them, it's just how things are and there is sensory overload which makes eating what normal people eat, very difficult.
I would definitely be seeking an ASD diagnosis. She sounds like she's got very big self-esteem issues and you need to remind her every day what a great person she is, how much you love her, how you'll always be there for her and how you believe in her. The chances are she doesn't believe in herself very much and thinks she's a loser and that's where a lot of this comes from. Teenage girls, particularly these days are so very very fragile.
Find some podcasts about self-esteem and coaching and listen to them yourself. It will help guide you about how to bolster her self-esteem.