This phase I trial studies the side effects and best dose of autologous T-antigen-presenting cells (T-APC) vaccine following therapeutic autologous lymphocytes (CTL) and cyclophosphamide in treating patients with metastatic melanoma. Aldesleukin may stimulate lymphocytes, such as CTL, to kill melanoma cells. Treating lymphocytes with aldesleukin in the laboratory may help the lymphocytes kill more tumor cells when they are put back in the body. Vaccines made from melanoma antigen may help the body build an effective immune response to kill tumor cells and may boost the effect of the CTL. Drugs used in chemotherapy, such as cyclophosphamide, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Giving T-APC vaccine after CTL and cyclophosphamide may be an effective treatment for melanoma