Initially your surgeon/cancer doctor made a diagnosis of a large tumor involving the skin or chest (T4) wall for your mother. I am sure the doctor, did scans to make sure that the cancer has not gone anywhere else (metastatic). In a patient with locally advanced cancer, involving skin or chest wall, the right treatment is chemotherapy before surgery. Before doing the chemo we usually do a core biopsy to do Estrogen and progesterone (ER/PR) receptor and Her-2 neu testing. Those tests are extremely important in the treatment of breast cancer. I did not see that in your report. But I am sure they did that.
After chemotherapy, she had a surgery and now the tumor is very small (about 3 cm). It has many other changes consistent with chemotherapy effect. So your mother's cancer cells were appropriately destroyed by the chemotherapy. That is clearly seen in the pathology (necrosis, inflammatory cells etc).
The report did not mention, if it is infiltrating ductal or explain if the lymph nodes were involved with cancer. As per the international standards, the pathology report should include a staging by the pathologist. But I think it could be pT2N0 (before your mother had T4N1). So it is an excellent outcome.
Your doctors treated your mother appropriately.
Now she needs radiation therapy (because of large initial tumor) and depending upon the ER/PR, she needs anti- estrogen pills. Depending upon the her-2 neu status, she can benefit from trastuzumab. You can take my recommendation to your doctor and ask them these questions.
I am sure your mother will do fine. She is in good hands.