Chemotherapy Hair Loss

My mother has a breast cancer. She went through the lumptectomy surgery twice to remove cancer. The infilterating cancer was very small 0.7cm (but DCS was 2cm). The report indicated negative for the lymph nodes and margin. But HER-2NIU test was positive. Then the doctor recommended Oncotype Assay test which revealed her score of 52, considered high for aggressiveness that means 34% chance of recurrence within next 10 years.

She has to decide between radiation therapy and chemotherapy. She is very scared of drugs and its side affects including hair loss etc.
Doctor says chemotherapy should help her in this case.
She is 65 years old. Is this a good treatment for her? Is there any other alternative treatment that is equally good that we can consider?

Please help us with your knowledge.

Many of the drugs used in chemotherapy cause loss of hair in the individual being treated. why such drugs affect hair growth.