I can understand the frustration with the levothyroxine.

It may be that going back on Synthroid might help. But also people with loss of thyroid from surgery tend to have problems afterword.

I know for myself, my left thyroid does not function 100%, from radio uptake testing. It is dead for some reason, infection or injury (I had receive some child abuse when young).
The part that remains can take up the slack. But I find when stressed, esp cold weather, I have about 2 wks of sluggish, depressed times. I have to wear leg warmers in winter sometimes.

T4 in levothyroxine supplementation is not the active form for the body to use. It has to be converted. Some people cannot do this efficiently. Zinc and Selenium are cofactors for this process.
If one is low in either, there can be problems with getting enough T3 for stressful times. Physical exertion, surgeries, cold exposure, illness are some stressors.

Also make sure she is taking it on an empty stomach....no food for at least an hour after. No calcium or other minerals at the same time (no milk, etc). Absorption from the GI tract is very sensitive and can be disrupted by any food/fiber present or minerals like calcium or iron etc.

In my years dispensing drugs, I have had many people who HATE Synthroid too... one had a reaction during surgery even blaming that brand. So it might not be the brand she is using, at all.
I use the generic Mylan. I am still on 75mcg and have been stable for several years now. But I do feel the onset of winter, painfully. My TSH remains at 2.0 or just below with every test.

People with gluten intolerance and other food intolerances may have an inflamed GI tract which may be making absorption erratic. Once the offending foods are removed, then things might stablize.

The severe constipation I have seen in patients with thyroidectomies.
It is a sign of severe hypothyroid functioning. This kind of thing, and including hair loss or orange skin pigmentation (which I had on my palms and feet) are signs that low thyroid is still present. You can broach and request some T3 (Cytomel) in this case. Some doctors will not give it, however. The natural thyroid is now unavailable thanks to our FDA and causing quite a problem with the millions who favor it over synthetic levothyroxine.