You are under no obligation to serve her.

Years ago, one bank I was working at, there was a customer in line loudly complaining about the bank, etc (to the other customers waiting). The manager asked him to leave, and he said "no". Manager asked the senior teller if she knew the customer, and she said yes. Manager told her [in front of the customers] to cut a check for the balance in his account, close the account and mail him the check to the address of record. He also gave the customer one of his business cards so he could spell the name correctly when he complained to management. Customer left - other customers and staff clapped! He apologized to the remaining customers and indicated that they and his staff were more important.