It is possible that she has adrenal problems along with thyroid problems. You mentioned that her cortisol was low as well as her blood sugar (both signs of adrenal fatigue or even more serious Addison's disease). If her adrenal glands are not able to keep up, then she will be tired, moody, etc. even if her thyroid levels are good. There is something called polyglandular syndrome (Schmidt's disease if it involves adrenals and thyroid). Post all her tests, the results, and the reference ranges here and we can look at them to get a better idea what may be going on. You might want to ask for more specific tests for cortisol such as an ACTH stim test to see whether or not she has enough reserves for stressful situations (thyroid hormones can even be a stressor to adrenals); possibly a saliva test to show her cortisol rhythm throughout the day (take 4 or more samples at different times in the day); and there are other tests. The Addison's board might help with any questions you may have about cortisol.
Anyway, I do believe she is hypothyroid for sure (4.4 is too high, especially with the presence of symptoms), but she most likely has something else compounding the problem. I would look into adrenal issues. Has she been checked for her iron levels and ferritin? Those might cause problems, too. I have read that cells need adequate cortisol and ferritin levels in order to even get thyroid hormones into the cells; otherwise it just circulates in the blood unused.