Can I Refuse to Turn Over Pension Payments to My Mother's Nursing Home?

No. It sounds like your mother's care is covered by Medicaid. Typically, nursing home residents who receive Medicaid must pay all but a small amount of their income to the nursing home and Medicaid picks up the balance of the cost. If you don't pay over all of the income, the nursing home could sue you for the money or it could seek to evict your mother for nonpayment. More likely, given the amount involved, the nursing home will be stuck with the loss, which doesn't seem fair.