1999 Ford Explorer housing unit for water pump

My car starter overheating 4 days ago. When I checked the radiator we noticed it hardly had any coolant so we refilled it. I had a friend who is a mechanic look at it and he said that it llooked like it was the system behind the water pump. A nother mechanic(the one that is going to do the actual work) told me that the part typically costs $500 at the dealership. He said its a plastic part that houses the water pump. As I am waiting to fix my car he said I could drive the car just check the coolant everyday. Well, when I went to drive my car it started to shake really bad at idle and worse as I tried to back up. It felt like it wanted to turn off when I pressed on the gas. Is the leak also causing the shaking? And is there such a thing as the housing unit for the water pump? I would really appreciate a prompt response I am scheduled to speak to the meachaninc this weekend (in 2 days).
Thank You
Veronica