What is wrong with my car and is it safe to drive?

I'm asking this again to try to get the right info so I can get a good answer. My car was leaking and steaming. My husband replaced the water pump but the car was still leaking. The problem was the timing cover and he did not feel like he could fix it. I am currently staying with my mother to take care of her. She talked me into letting a family friend fix the car. After the guy had the car my mother told me a story about how he had fixed a car for her, messed up the timing belt and ruined the car. So, obviously I was upset because the problem with my car involves the timing.

My husband was visiting this weekend and he took the car for a test drive. He says that the car is idling rough and lacks power to accelerate. He says that he can feel the engine vibrating when he pushes on the gas pedal.

So, since my car was okay before this happened, I am assuming that either something else was damaged because my car overheated or the guy who worked on it did something wrong. What might be wrong with my car and would it be safe for me to drive the car 3 hours home when the time comes. My husband feels more comfortable having our regular mechanic fix the car since we don't know anything about the mechanics in this area.