A 14-year-old girl with a history of bilateral retinoblastoma (treated with chemotherapy and radiation 10 years ago) presents with a 2-month history of pain and swelling in the proximal tibia. Radiographs reveal a mixed lytic and sclerotic lesion in the metaphyseal region with cortical breakthrough and soft tissue extension. A biopsy shows malignant spindle cells producing osteoid and bone. What is the most likely diagnosis, and what is the key pathogenic mechanism underlying her predisposition?