RATIONALE: Drugs used in chemotherapy, such as docetaxel and carboplatin, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Monoclonal antibodies, such as trastuzumab, can block tumor growth in different ways. Some block the ability of tumor cells to grow and spread. Others find tumor cells and help kill them or carry tumor-killing substances to them. Lapatinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Giving docetaxel together with carboplatin, trastuzumab, and lapatinib may kill more tumor cells. PURPOSE: This phase II trial is studying the side effects of giving docetaxel together with carboplatin, trastuzumab, and lapatinib in treating patients with early stage breast cancer.

OBJECTIVES: Primary * Determine the safety and tolerability (including the rate of diarrhea) of adjuvant therapy comprising docetaxel, carboplatin, trastuzumab (Herceptin®), and lapatinib ditosylate in patients with early-stage breast cancer. Secondary * Evaluate the adverse event profile of this regimen in these patients. * Evaluate LVEF in patients receiving this regimen. OUTLINE: Patients receive docetaxel IV over 60 minutes and carboplatin IV over 30 minutes on day 1, trastuzumab (Herceptin®) IV over 30-90 minutes on days 1, 8, and 15, and oral lapatinib ditosylate on days 1-21 (TCHL). Treatment with TCHL repeats every 3 weeks for 6 courses in the absence of disease progression or unacceptable toxicity. Patients then receive trastuzumab IV over 30-90 minutes on day 1 and oral lapatinib ditosylate on days 1-21 (days 1-7 of course 12 only) (LT). Treatment with LT repeats every 3 weeks for 12 courses in the absence of disease progression or unacceptable toxicity.. After completion of study treatment, patients are followed every 6 months for 2 years and then annually for up to 8 years.