Hmm. Seems like your mother's doctor is in full "Blame the Patient" mode.
As well as suspecting she is under-medicated and almost certainly has low Free T3 I also suspect your mother is very low on nutrients.
Levothyroxine is a synthetic version of thyroxine (otherwise known as T4), a hormone that thyroids produce. It has little or no activity of its own.
The T4 has to be converted in the body into the active hormone T3. It is low T3 that makes people feel hypothyroid (underactive) and high T3 that makes people feel hyperthyroid (overactive).
A healthy thyroid produces some T3 directly. The rest of the T3 the body needs is made by converting T4 in muscles and organs around the body. One of the biggest users of T3 is the brain. The heart needs plenty too.
Doctors rarely measure T3. They say it isn't important (!!!) and it fluctuates too much to be worth measuring. But if your mother's thyroid can't produce much (or any) T3 and she can't convert T4 into T3 very well, then she will be very low in it. Without measuring it the doctors will never know.
In order to convert T4 into T3 the body needs good levels of nutrients. The problem is that hypothyroidism reduces stomach acid and makes it harder to extract minerals and vitamins from food.
The nutrients that are vital to conversion are vitamin B12, vitamin D, folate and ferritin (iron stores).
These nutrients need to be at optimal levels, not just within the reference range. So for example a level of ferritin of 15 ug/L with a reference range of (15 - 150) would be classed as "normal" by the NHS and no treatment would be offered. But hypothyroid people need the levels to be optimal. For ferritin, with the reference range I've given, this would be around 80 - 100. Some people feel best slightly above this, with a level of 100 - 120.
Note that optimal is not the same for every nutrient.
So, you need to find out the levels of your mother's nutrients and supplement where necessary. You also need to find out her Free T3. The NHS rarely prescribes T3, but it can legally be bought online and imported for personal use. Many of the hypothyroid people who are left to suffer by the NHS do this so that we can have a life.
If you can get results from your mother's doctor, great. If you can't there are ways and means of getting tested privately without involving a doctor.
By the way, low vitamin B12 and low Free T3 are two causes of dementia-like symptoms which are actually reversible if they are dealt with in time.