Some videos that may be helpful. Gist of it all is the liver/adrenals/gall bladder not functioning properly can all lead to low thyroid activity which then causes other problems. Could be relevant to you (with hypo symptoms) and Mrs. Konstantin, as you mentioned estrogen issue suspected.
high estrogen ---> low thyroid
adrenal (high cortisol) issues ----> low thyroid
liver issues ------> low thyroid
This may account for why some people are having much easier time with iodine, as they've already had good cleaning through diet, supplements, etc., which cleaned the body and already had thyroid functioning better, whether they knew it or not. That would make the detox much smoother when iodine starts kicking halides/metals out.
If those organs are already impaired by bad diet, toxin buildup, etc., then adding iodine detox just overwhelms them all.
Many of pieces of a puzzle to put together.
These first two videos do a good job of showing the whole picture/relationship.
How to Have a Healthy Thyroid
__https://www.youtube.com/watch?v=BTNhlkOW9qc
How to Heal Thyroid and Adrenal Fatigue
__https://www.youtube.com/watch?v=F1rxW9IzYrA
The next three go into detail on each "link/interaction." He does have products for sale which he briefly mentions, but they are not "sales pitch" videos.
The Thyroid Gland and the Estrogen Connection
__https://www.youtube.com/watch?v=GgfWsp0hqYc&list=PLVLP-bhbxACZ322PIWZ-FBvXzjqUBtG4I&index=2
What's Really Behind a Sluggish Thyroid Problem
__https://www.youtube.com/watch?v=pm49uFWTYBI&index=7&list=PLVLP-bhbxACZ322PIWZ-FBvXzjqUBtG4I
Most Thyroid Issues Are Secondary to Other Problems
__https://www.youtube.com/watch?v=IdDMMs96N9A
Overall might want to consider doing the meds first, while taking probiotics and cleaning up diet as much as you can. Then in conjunction with diet, cleansing liver/address adrenal issues (which will begin helping the thyroid, which will then help other body functions). Might be surprised how many issues are improved just doing that. Then, add iodine after all that is functioning better.
Of course, you've got issues in implementing all of those, but the last thing you want is additional symptoms/detox from adding iodine before the body can handle it, thereby minimizing anything which could possibly turn her away from any holistic/natural therapies.
You can also "prime the pump" for a while before beginning the iodine with supplements which, IIRC, are basically the iodine cofactors, plus vits a, e, lots of c, and omega 3. I can't find the list just now I but it's out there. Lynne Farrow talks about this in interviews.
Best of luck and hope she's feeling better soon!