When i was diagnosed with graves/hyperthyroidism, i did the radiation treatment, but it did not work for me. Graves affects a lot of the body, not just the thyroid, it started attacking my entire organs. Make sure she takes the medication, but if she can not keep it down i would call the doctor. I ended up getting a thyroidectomy, it worked for me. I do take one tiny pill a day and will for the rest of my life, but all my symptoms went away.
I don't have any insight in this disease. Just wanted to tell you your sister is blessed to have someone care enough about her to do what you have done here.
Being a thyroid problem pt, I do know it is DIFFICULT to put it mildly, to find a good dr to properly treat, and is knowledgeable in all the lab values and what they mean as far as medicine levels and things like that.
You have to be extremely proactive, almost demanding to get anything done. In order to do that, you have to research, research, research. And in the middle of this the pt usually does not feel like having these confrontations with the dr, so they are not properly treated. That is why the pt needs an advocate.
I am sure someone will be along with some ideas on your question, just wanted to put my 2 cents in.