Your daughter's antibody result shows the reason for the hypothyroidism - she has an autoimmune condition called hashimoto's thyroiditis. This doesn't affect her treatment. The result that really affects her is the FT3 result, which is less than half way up the range. T3 is the active hormone the body needs.
There are several possible issues here. She could take a little more Thyroxine - 50mcg is a starting dose and because the antibodies and attacking here thyroid it will gradually stop producing hormone so she will gradually need more hormone replacement. However the TSH result is at 1.01 which is not high enough for a doctor to allow her an increase. Did she have the test done first thing in the morning, having not taken Thyroxine for 24 hours before the test?
She may not be converting T4 into T3 very well. Her FT4 level is just over half way up the range, so there is probably enough of this for her body to use. Her levels of Ferritin and B12 can affect conversion, and her levels of Vitamin D should be also checked because people with hypothyroidism often end up deficient.
Some people would consider adding a little T3 to her Levothyroxine, but doctors don't like doing this because it is expensive. People often buy their own, or switch to NDT (Natural dessicated thyroid) because it contains T4 and T3, but this often annoys doctors.
People with one autoimmune disease often end up with others, so it's worth her doctor ruling out pernicious anaemia, lupus, diabetes and various other conditions.
Otherwise her symptoms could of course be due to something completely unrelated to thyroid.