Sigh. I have been vegetarian and vegan at times, and had my DS 8+ years ago. I suppose it's possible to do it (not vegan, maybe vegetarian) but it was work, like a full time job. The amount of effort it would take to remain vegetarian as a DSer is not worth it. I eat meat.
I am a diligent DSer, meaning I don't ever miss getting my labs, and those labs are scrutinized to make sure I keep levels in good range, and at the earlier stages of my DS when I still played with the idea of being vegetarian, I had my labs drawn every 3 months. Insurance didn't pay for all those, so I had to pay thousands out of pocket. I didn't find a DR that was well versed in the DS, so I found a young, eager to learn Dr, that wanted to learn along with me. I still go to her.
It takes time finding the right Drs, or fighting for referrals to the right type (like an endo) time researching what we need (as Drs still don't have many of the answers for us), time to continually fiddle with lab results and adjusting supplements, money to throw at tests or dr visits or supplements, and time to research, and come to sites like this one to learn.
It sounds like your daughter is at the opposite end of the diligence scale as me regarding her DS. I won't try the vegetarian thing again, and certainly think she shouldn't.
I'm concerned about your daughter and that she is causing ever more health issues which may not be reversible, or fatal. This is one of the more knowledgeable communities (and more importantly, poor information is weeded out) available online. Could you convince her to come here and learn?
By the way, kudos to you for coming here to try to gain some information for her, and finding a place with good DS information. I hope she can care enough to come here for herself.