Chevy Corsica Girlfriend's Corsica. Jerks!

Engine Mechanical problem
Chevy Corsica 6 cyl Front Wheel Drive Automatic

This might be two problems, but I don't know. First one: this happens when the car is driven a long distance on the highway (about an hour or more). When the car is slowed down, and then stopped at a light (when exiting the freeway after a long drive) the car will shake really bad, and die. When you try to start it again and get on the gas, it will die repeatedly. It normally takes 4 or 5 times before it will work. I thought it might have been that the auto transmission was refusing to shift back down to first, but I don't know.

second problem: (I was not here when this happened, so it is just based on what she told me) when driving on the highway, the car has recently started to do some type of jerking once in a while. She said it happens when she is going about 70. Out of nowhere is will start to jerk (almost like it was speeding up and slowing down slightly, from what she told me). I don't know. But she seemed to have the impression that it might have been related to cruise control. Not for sure though.