I would sending teammate in my office and try,i, with less nerves to resolve the problem...i would be a little bit with the client's part,for his eyes and only,so i could calm him down and when i will finish with him i would discuss to the office with my coleegue the details and how to act in this situations...
Customer is the King, always, and without your teammate you are doomed. The king cannot be served appropriately. Such situations arises once and then. Every situaton must tackle on the ground reality and current scenario basis. Either the customer or the teammate feel being pushed aside...